Subjects -> MATHEMATICS (Total: 1075 journals)
    - APPLIED MATHEMATICS (86 journals)
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    - MATHEMATICS (794 journals)
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MATHEMATICS (794 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 12)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 6)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 2)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 4)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 2)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 7)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 9)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 7)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access  
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 4)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 8)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 14)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Uncertainty Analysis and Applications     Open Access  
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
Journal of Water and Land Development     Open Access   (Followers: 3)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 4)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 1)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 5)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 1)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 23)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal  
Logic Journal of the IGPL     Hybrid Journal  
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematika     Open Access  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Open Access   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 1)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 3)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 1)
Mathematics Education Research Journal     Partially Free   (Followers: 17)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 7)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MATI : Mathematical Aspects of Topological Indeces     Open Access  
MATICS     Open Access   (Followers: 2)
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal  
Metascience     Hybrid Journal   (Followers: 1)
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 1)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 3)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)
North Carolina Journal of Mathematics and Statistics     Open Access  
North-Holland Mathematical Library     Full-text available via subscription   (Followers: 1)
North-Holland Mathematics Studies     Full-text available via subscription  
North-Holland Series in Applied Mathematics and Mechanics     Full-text available via subscription   (Followers: 1)
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 4)
Numeracy : Advancing Education in Quantitative Literacy     Open Access  
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 2)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerical Mathematics : Theory, Methods and Applications     Full-text available via subscription  
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 5)
Open Journal of Modelling and Simulation     Open Access   (Followers: 1)

  First | 1 2 3 4     

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Journal Cover
Nonlinear Analysis: Real World Applications
Journal Prestige (SJR): 1.627
Citation Impact (citeScore): 2
Number of Followers: 2  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1468-1218 - ISSN (Online) 1468-1218
Published by Elsevier Homepage  [3206 journals]
  • Minimization principles for elliptic hemivariational inequalities
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Weimin Han
       
  • The anisotropic regularity criteria for 3D Navier–Stokes equations
           involving one velocity component
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Chenyin Qian
       
  • Large time behavior of solutions to a quasilinear attraction–repulsion
           chemotaxis system with logistic source
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Xiao He, Miaoqing Tian, Sining Zheng
       
  • A generalized infectious model induced by the contacting distance (CTD)
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Zhihui Ma, Shufan Wang, Xiaohua LiAbstractThe aim of this paper is to theoretically study the effect of the contacting distance (CTD) between the susceptible and infectious individuals in controlling infectious diseases. This paper formulates a generalized SEIR model incorporating the effect of the contacting distance (CTD). The dynamical behaviors of the proposed model are investigated and the controlling measures of the infectious diseases are developed. The results show that the contacting distance (CTD) between the susceptible and infectious individuals plays an important role in controlling infectious diseases. Some diseases will be globally controlled when the contacting distance (CTD) is larger than the threshold value. That is to say, the long contacting distance (CTD) implies the corresponding diseases will be controlled. However, for other diseases, the long or short contacting distance (CTD) will induce them to spread and be endemic. The moderate contacting distance (CTD) may be beneficial to control these diseases. Therefore, the appropriate contacting distance (CTD) should be selected for the given diseases in order to control the corresponding infectious diseases. Finally, a special numerical experiment is given to test our results. These results give some theoretical and experimental guides for the disease control authorities.
       
  • Hopf bifurcation at infinity in 3D symmetric piecewise linear systems.
           Application to a Bonhoeffer–van der Pol oscillator
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): E. Freire, E. Ponce, J. Ros, E. Vela, A. AmadorAbstractIn this work, a Hopf bifurcation at infinity in three-dimensional symmetric continuous piecewise linear systems with three zones is analyzed. By adapting the so-called closing equations method, which constitutes a suitable technique to detect limit cycles bifurcation in piecewise linear systems, we give for the first time a complete characterization of the existence and stability of the limit cycle of large amplitude that bifurcates from the point at infinity. Analytical expressions for the period and amplitude of the bifurcating limit cycles are obtained. As an application of these results, we study the appearance of a large amplitude limit cycle in a Bonhoeffer–van der Pol oscillator.
       
  • Traveling wave solutions for a predator–prey system with two
           predators and one prey
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chin-Chin WuAbstractWe study a predator–prey model with two alien predators and one aborigine prey in which the net growth rates of both predators are negative. We characterize the invading speed of these two predators by the minimal wave speed of traveling wave solutions connecting the predator-free state to the co-existence state. The proof of the existence of traveling waves is based on a standard method by constructing (generalized) upper-lower-solutions with the help of Schauder’s fixed point theorem. However, in this three species model, we are able to construct some suitable pairs of upper-lower-solutions not only for the super-critical speeds but also for the critical speed. Moreover, a new form of shrinking rectangles is introduced to derive the right-hand tail limit of wave profile.
       
  • Dynamics of adaptation in an anisotropic phenotype-fitness landscape
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): F. Hamel, F. Lavigne, G. Martin, L. RoquesAbstractWe study the dynamics of adaptation of a large asexual population in a n-dimensional phenotypic space, under anisotropic mutation and selection effects. When n=1 or under isotropy assumptions, the ‘replicator-mutator’ equation is a standard model to describe these dynamics. However, the n-dimensional anisotropic case remained largely unexplored.We prove here that the equation admits a unique solution, which is interpreted as the phenotype distribution, and we propose a new and general framework to the study of the quantitative behaviour of this solution. Our method builds upon a degenerate nonlocal parabolic equation satisfied by the distribution of the ‘fitness components’, and a nonlocal transport equation satisfied by the cumulant generating function of the joint distribution of these components. This last equation can be solved analytically and we then get a general formula for the trajectory of the mean fitness and all higher cumulants of the fitness distribution, over time. Such mean fitness trajectory is the typical outcome of empirical studies of adaptation by experimental evolution, and can thus be compared to empirical data.In sharp contrast with the known results based on isotropic models, our results show that the trajectory of mean fitness may exhibit (n−1) plateaus before it converges. It may thus appear ‘non-saturating’ for a transient but possibly long time, even though a phenotypic optimum exists. To illustrate the empirical relevance of these results, we show that the anisotropic model leads to a very good fit of Escherichia coli long-term evolution experiment, one of the most famous experimental dataset in experimental evolution. The two ‘evolutionary epochs’ that have been observed in this experiment have long puzzled the community: we propose that the pattern may simply stem from a climbing hill process, but in an anisotropic fitness landscape.
       
  • Persistence and extinction of nonlocal dispersal evolution equations in
           moving habitats
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Patrick De Leenheer, Wenxian Shen, Aijun ZhangAbstractThis paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed c. It is shown that the species becomes extinct if the moving speed c is larger than the so called spreading speed c∗, where c∗ is determined by the maximum linearized growth rate function. If the moving speed c is smaller than c∗, it is shown that the persistence of the species depends on the patch size of the habitat, namely, the species persists if the patch size is greater than some number L∗ and in this case, there is a traveling wave solution with speed c, and it becomes extinct if the patch size is smaller than L∗.
       
  • Global existence and asymptotic dynamics in a 3D fractional chemotaxis
           system with singular sensitivity
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Kerui Jiang, Zuhan Liu, Ling ZhouAbstractIn this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates.
       
  • Multiplicity of clines for systems of indefinite differential equations
           arising from a multilocus population genetics model
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Guglielmo Feltrin, Paolo GidoniAbstractWe investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of the Neumann boundary value problem p1′′+λ1w1(x,p2)f1(p1)=0,in Ω,p2′′+λ2w2(x,p1)f2(p2)=0,in Ω,p1′=p2′=0,on ∂Ω,where the coupling-weights wi are sign-changing in the first variable, and the nonlinearities fi:[0,1]→[0,+∞[ satisfy fi(0)=fi(1)=0, fi(s)>0 for all s∈]0,1[, and a superlinear growth condition at zero. Using a topological degree approach, we prove existence of 2N positive fully nontrivial solutions when the real positive parameters λ1 and λ2 are sufficiently large.
       
  • Modeling and analysis of recurrent autoimmune disease
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Yancong Xu, Yu Yang, Fanwei Meng, Pei YuAbstractIn this paper, we consider dynamics and bifurcations in two HIV models with cell-to-cell interaction. The difference between the two models lies in the inclusion or omission of the effect of involvement. Particular attention is focused on the effects due to the cell-to-cell transmission and the effect of the involvement. We investigate the local and global stability of equilibria of the two models and give a comparison. We derive the existence condition for Hopf bifurcation and prove no Bogdanov-Takens bifurcation in this system. In particular, we show that the system exhibits the recurrence phenomenon, yielding complex dynamical behavior. It is also shown that the effect of the involvement is the main cause of the periodic symptoms in HIV or malaria disease. Moreover, it is shown that the increase of cell-to-cell interaction may be the main factor causing Hopf bifurcation to disappear, and thus eliminating oscillation behavior. Finally, numerical simulations are present to demonstrate our theoretical results.
       
  • Stability and cross-diffusion-driven instability in a diffusive
           predator–prey system with hunting cooperation functional response
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Danxia Song, Chao Li, Yongli SongAbstractThis paper presents a qualitative study of a diffusive predator–prey system with the hunting cooperation functional response. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium are explicitly determined. It is shown that the hunting cooperation affects not only the existence of the positive equilibrium but also the stability. For the diffusive system, the stability and cross-diffusion driven Turing instability are investigated according to the relationship of the self-diffusion and the cross-diffusion coefficients. Stability and cross-diffusion instability regions are theoretically determined in the plane of the cross-diffusion coefficients. The technique of multiple time scale is employed to deduce the amplitude equation of Turing bifurcation and then pattern dynamics driven by the cross-diffusion is also investigated by the corresponding amplitude equation.
       
  • On a class of nonlinear stochastic integral equations
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): R. NegreaAbstractWe prove some existence and uniqueness results for a nonlinear stochastic integral equation using fixed-point theory methods to ensure the convergence of the successive approximations to the unique random solution.
       
  • Decay rates of solutions to Euler equations with time-dependent damping
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Lina ZhangAbstractIn this paper, we are concerned with the isentropic Euler equations with time-dependent damping like −μ1+tρu for physical parameter μ>0. By using the technical time-weighted energy method, the global existence is proved and the decay estimates are obtained for the solutions of Euler equations. It is interesting that the new decay estimates are dependent on the physical parameter μ. And the decay rates are much better than that obtained by Pan.
       
  • Qualitative analysis on a diffusive age-structured heroin transmission
           model
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Xi-Chao Duan, Xue-Zhi Li, Maia MartchevaAbstractIn this paper, to understand the impact of spatial heterogeneity of treatment and movement of individuals on the persistence and extinction of heroin spread, we propose a new diffusive heroin transmission model with treatment-dependent age-structure. The basic reproduction number in heterogenous environment R0 of the system is defined, which is consistent with the one deduced from the next generation operator approach R(x). The threshold dynamics in terms of the basic reproduction number is established: if R0≤1, the drug-free steady state is globally asymptotically stable, if R0>1, heroin transmission is uniformly persistent if it is present initially. In particular, when the environment is homogeneous and R0>1, our system has a unique space-independent drug spread steady state and it is globally asymptotically stable. Finally, some numerical simulations are carried out to illustrate the main results.
       
  • Global solutions to The Vlasov–Poisson–Boltzmann system with
           weak angular singularity
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Yingzhe Fan, Ping XuAbstractWe prove the global existence of smooth solutions near Maxwellians to the Cauchy problem of non-cutoff Vlasov–Poisson–Boltzmann equation for soft potentials, provided that the weak angular singularity assumption holds and the algebraic decay initial perturbation is sufficiently small. This extends the work of Duan and Liu (2013), in which the case of the strong angular singularity 12≤s
       
  • Mathematical analysis and optimal control of a cholera epidemic in
           different human communities with individuals’ migration
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Eric Kokomo, Bongor Danhrée, Yves EmvuduAbstractWe propound a deterministic, nonlinear model for the transmission dynamics of cholera in different human communities with individuals’ migration. The considered different human communities are crossed by a running water which is contaminated by the vibrio cholerae bacterium. The formulated model for each community which is an initial/boundary-value problem constituted of four parabolic partial differential equations, integrates antibiotic treatment, hydration therapy and contaminated water treatment as control mechanisms of the disease. Using semigroup theory, we prove that this model has a unique bounded positive solution. Also under a given condition, the existence of a trivial equilibrium and of a nontrivial equilibrium of each community is established and their local and global stabilities are studied. In analysis of Turing’s instability, we determine sufficient conditions allowing the formation of a spatially stationary and periodic heterogeneous pattern. Analytically the existence of a unique optimal control is established by the use of functional analysis techniques and an optimal control θ̄ is determined to eradicate the epidemic in each community. In order to confirm our theoretical results, we finish with a real-world application concerning the cholera epidemic that took place in Cameroon in 2011.
       
  • Strong solutions to compressible–incompressible two-phase flows with
           phase transitions
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Keiichi WatanabeAbstractWe consider a free boundary problem of compressible–incompressible two-phase flows with phase transitions in general domains of N-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier–Stokes–Korteweg equations and the Navier–Stokes equations, respectively. This paper shows that for given T>0 the problem admits a unique strong solution on (0,T) in the maximal Lp−Lq regularity class provided the initial data are small in their natural norms.
       
  • Existence and uniqueness of solution of free boundary problem with
           partially degenerate diffusion
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Siyu Liu, Mingxin WangAbstractIn this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
       
  • Complicated oscillations and non-resonant double Hopf bifurcation of
           multiple feedback delayed control system of the gut microbiota
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Lijun Pei, Yameng Chen, Shuo WangAbstractIn this paper, we consider the complex dynamics of a novel mathematical model for a feedback control system of the gut microbiota, which was proposed by Dong, et al. The main work of the present paper is to study the effect of antibiotics injection on the gut microbiota through some dynamical methods, such as double Hopf bifurcation analysis and so on. We first use DDE-BIFTOOL to find the non-resonant double Hopf bifurcation points of the system, and draw the bifurcation diagram with two bifurcation parameters, τ1 and τ2, i.e., respective measurement delays. Then we study small perturbations of two delay differential equations at these double Hopf bifurcation points, and the method of multiple scales is employed to obtain two common complex amplitude equations. By analyzing the amplitude equations, we can derive the classification and unfolding of these double Hopf bifurcation points. Finally, we verify the results by numerical simulations. We find more complicated dynamic behaviors of the system via analytical method. For example, there exists stable equilibrium, stable periodic solution or even the co-existing stable periodic solutions in respective region. And the numerical simulations are consistent with the analytic results, meanwhile it implies that the MMS is effective and accurate. All complex dynamical phenomena found in the present paper can be very helpful for the researchers to understand the mechanism of the system of gut microbiota. And it is also very significant to microbiology and engineering control. It reveals that the measurement delays can induce the complicated dynamics in this system and to the ends of excellent performance, we should take the proper values of these delays.
       
  • A sub-supersolution approach for Neumann boundary value problems with
           gradient dependence
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Dumitru Motreanu, Angela Sciammetta, Elisabetta TornatoreExistence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems.
       
  • Radial stability of periodic orbits of damped Keplerian-like systems
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Zaitao Liang, Fangfang LiaoAbstractIn this paper, by using the third order approximation method, the averaging method and the theory of upper and lower solutions, we study the existence and radial stability of periodic orbits of damped Keplerian-like systems. Two different results are obtained: perturbative and global results. Our results are also applicable to the classical Keplerian-like systems.
       
  • Existence of weak solutions to the Keller–Segel chemotaxis system with
           additional cross-diffusion
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Gurusamy Arumugam, André H. Erhardt, Indurekha Eswaramoorthy, Balachandran KrishnanAbstractIn this paper, we consider the Keller–Segel chemotaxis system with additional cross-diffusion term in the second equation. This system is consisting of a fully nonlinear reaction–diffusion equations with additional cross-diffusion. We establish the existence of weak solutions to the considered system by using Schauder’s fixed point theorem, a priori energy estimates and the compactness results.
       
  • Miridae control using sex-pheromone traps. Modeling, analysis and
           simulations
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): M. Djoukwe Tapi, L. Bagny-Beilhe, Y. DumontAbstractCocoa mirid, Sahlbergella singularis, is known to be one of the major pests of cocoa in West Africa. In this paper, we consider a biological control method, based on mating disrupting, using artificial sex pheromones, and trapping, to limit the impact of mirids in plots. We develop and study a piece-wise smooth delayed dynamical system. Based on previous results, a theoretical analysis is provided in order to derive all possible dynamics of the system. We show that two main threshold parameters exist that will be useful to derive long term successful control strategies for different level of infestation. We illustrate and discuss our results when cacao pods production is either constant along the year or seasonal. To conclude, we provide future perspectives based on this work.
       
  • Global existence and asymptotic stability in a predator–prey
           chemotaxis model
    • Abstract: Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Shengmao Fu, Liangying MiaoAbstractIn this paper, we consider the global behavior of the fully parabolic predator–prey chemotaxis model u1t=d1Δu1+χ∇⋅(u1∇v)+μ1u1(1−u1−e1u2),x∈Ω,t>0,u2t=d2Δu2−ξ∇⋅(u2∇v)+μ2u2(1+e2u1−u2),x∈Ω,t>0,vt=d3Δv+αu1+βu2−γv,x∈Ω,t>0,∂u1∂ν=∂u2∂ν=∂v∂ν=0,x∈∂Ω,t>0,u1(x,0)=u1,0(x),u2(x,0)=u2,0(x),v(x,0)=v0(x),x∈Ωin a smooth bounded domain Ω⊂Rn, where d1,d2,
       
  • Trajectory statistical solutions for the 3D Navier–Stokes equations: The
           trajectory attractor approach
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Caidi Zhao, Yanjiao Li, Zhongchun SongAbstractIn this article, we construct the trajectory statistical solution for the 3D incompressible Navier–Stokes equations via the natural translation semigroup and trajectory attractor. In our construction, the trajectory statistical solution is an invariant space–time probability measure which is carried by the trajectory attractor of the natural translation semigroup defined on the trajectory space, and the trajectory statistical solution possesses the invariant property under the acting of the translation semigroup.
       
  • Global dynamics of nonautonomous Hindmarsh–Rose equations
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Chi Phan, Yuncheng YouAbstractGlobal dynamics of nonautonomous diffusive Hindmarsh–Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback dissipative property and the pullback asymptotical compactness. Then the existence of pullback exponential attractor is also established by proving the smoothing Lipschitz continuity in a long run of the solution process.
       
  • Existence of a time periodic solution for the compressible Euler equation
           with a time periodic outer force
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Naoki TsugeAbstractWe are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time periodic solution. Although this is a fundamental problem for other equations, it has not been received much attention for the system of conservation laws until now.When we prove the existence of the time periodic solution, we face with two problems. One is to prove that initial data and the corresponding solutions after one period are contained in the same bounded set. To overcome this, we employ the generalized invariant region, which depends on the space variables. This enable us to investigate the behavior of solutions in detail. Second is to construct a continuous map. We apply a fixed point theorem to the map from initial data to solutions after one period. Then, the map needs to be continuous. To construct this, we introduce the modified Lax–Friedrichs scheme, which has a recurrence formula consisting of discretized approximate solutions. The formula yields the desired map. Moreover, the invariant region grantees that it maps a compact convex set to itself. In virtue of the fixed point theorem, we can prove a existence of a fixed point, which represents a time periodic solution. Finally, we apply the compensated compactness framework to prove the convergence of our approximate solutions.
       
  • Spatial-temporal risk index and transmission of a nonlocal dengue model
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Min Zhu, Zhigui Lin, Lai ZhangAbstractThe nonlocal incidence and free boundaries are introduced into a classic SIR-SI model describing the transmission dynamics of dengue fever, where the nonlocal incidence allows for interactions of susceptible population at a given location with infected mosquitoes in the whole area, and free boundaries represent the expanding front of the area contaminated by dengue virus. We derive a spatial–temporal risk index in terms of the basic reproduction number, which depends on the nonlocal incidence and time variable. More importantly, we explore the relationships between different model variants regarding these risk indices. We additionally find sufficient conditions to ensure the vanishing and spreading of dengue fever, and demonstrate, for a special case, the asymptotic behavior of its solution when spreading occurs. Finally, we carry out numerical simulations to demonstrate our analytical findings and further provide their epidemiological explanations.
       
  • The dynamics of a zooplankton–fish system in aquatic habitats
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yu Jin, Feng-Bin WangAbstractDiel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this paper, we use a temporally periodic reaction–diffusion–advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface water during the night. We establish the persistence theory for both species as well as the existence of a time-periodic positive solution to investigate how zooplankton manage to maintain a balance with their predators via vertical migration. Numerical simulations discover the effects of migration strategy, advection rates, domain boundary conditions, as well as spatially varying growth rates, on persistence of the system.
       
  • Continuity of periodic solutions of the Landesman–Lazer equation in
           external forces
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yaru Dou, Gang MengAbstractIn this paper we study the continuity of periodic solutions of the Landesman–Lazer equations in coefficient functions. It will be proved that these periodic solutions are not only continuous in coefficient functions with respect to the usual Lp topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are the basis to study some quantities defined from solutions in a quantitative way.
       
  • Large time behavior for the support of momentum density of the
           Holm–Staley b-family equation with weakly dissipative term
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Lu Cao, Zaihong Jiang, Mingxuan ZhuAbstractIn this paper, we study the Holm–Staley b-family equation with weakly dissipative term. Firstly, we show the infinite propagation speed that if the initial datum u0(x) has a compact support, the corresponding solution u(x,t) does not have a compact x-support any longer in its lifespan. Then, we obtain the large time behavior of the support of momentum density with the initial data compact supported.
       
  • A global mathematical model of malaria transmission dynamics with
           structured mosquito population and temperature variations
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Bakary Traoré, Ousmane Koutou, Boureima SangaréAbstractIn this paper, a mathematical model of malaria transmission which takes into account the four distinct mosquito metamorphic stages is presented. The model is formulated thanks to the coupling of two sub-models, namely the model of mosquito population and the model of malaria parasite transmission due to the interaction between mosquitoes and humans. Moreover, considering that climate factors have a great impact on the mosquito life cycle and parasite survival in mosquitoes, we incorporate seasonality in the model by considering some parameters which are periodic functions. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on two biological insightful quantities : the vector reproduction ratio Rv and the basic reproduction ratio R0. Indeed, if Rv1 and R01 and R0>1 the disease remains persistent. Finally, using the reported monthly mean temperature of Burkina Faso, we perform some numerical simulations to illustrate our theoretical results.
       
  • Erratum to “On the Cauchy problem for a model equation for shallow water
           waves of moderate amplitude” [Nonlinear Anal. RWA 14 (5) (2013)
           2022–2026]
    • Abstract: Publication date: Available online 12 December 2019Source: Nonlinear Analysis: Real World ApplicationsAuthor(s): N. Duruk MutlubaşAbstractThe local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime was proved in Duruk Mutlubaş (2013). In this paper, we correct the mistake made in the proof of the main result and give the appropriate assumptions and corresponding results.
       
  • Global solutions to 3-D Navier–Stokes–Maxwell system slowly
           varying in one direction
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Gaocheng YueAbstractThe present paper is devoted to the well-posedness issue of solutions of a full system of the 3-D incompressible magnetohydrodynamic (MHD) equations with large initial velocity and magnetic field slowly varying in one space variable. By means of the anisotropic Littlewood–Paley analysis we prove the global well-posedness of solutions in the framework of anisotropic type Besov spaces for ϵ and σ sufficiently small. Toward this and due to the divergence-free property of magnetic field, the proof is based on unified energy estimates which is valid for the magnetic field satisfying the inhomogeneous damped wave equation.
       
  • Large time behaviors of solutions to the unipolar hydrodynamic model of
           semiconductors with physical boundary effect
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hui Sun, Ming Mei, Kaijun ZhangAbstractIn this paper, we study the asymptotic behaviors in time of solutions to the unipolar hydrodynamic model of semiconductors in the form of Euler–Poisson equations on the half line with the boundary effect, where the boundary conditions are proposed physically as the inflow/outflow/impermeable boundary or the insulating boundary. Different from the Cauchy problem, the boundary effect causes some essential difficulties in determining the asymptotic profiles for the solutions and occurs the boundary layers. First of all, by heuristically analyzing, we reasonably propose some additional boundary conditions at far field to the corresponding steady-state equations such that the steady-state systems are well-posed. Thus, we can determine the corresponding steady-states as the expected asymptotic profiles for the solutions of original IBVPs. Secondly, there are some L2-boundary-layers between the solutions of original IBVPs and their steady-states. After investigating the exact form of gaps, we technically construct some correction functions to delete these gaps. Finally, by using the energy estimates, we further prove that the original solutions of the inflow/outflow/impermeable problem (insulating problem) time-exponentially (time-exponentially/algebraically) converge to their asymptotic profiles. Finally, we carry out some numerical simulations, which show that, the graphs for the asymptotic profiles in different boundary cases are significantly distinct.
       
  • Eco-epidemiological model with fatal disease in the prey
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): David Greenhalgh, Qamar J.A. Khan, Fatma Ahmed Al-KharousiAbstractWe investigate a model consisting of a predator population and both susceptible and infected prey populations. The predator can feed on either prey species but instead of choosing individuals at random the predator feeds preferentially on the most abundant prey species. More specifically we assume that the likelihood of a predator catching a susceptible prey or an infected prey is proportional to the numbers of these two different types of prey species. This phenomenon, involving changing preference from susceptible to infected prey, is called switching. Mukhopadhyay studied a switching model and proposed that the interaction of predators with infected prey is beneficial for the growth of the predator. In this model, we assume that the predator will eventually die as a result of eating infected prey. We find a threshold parameter R0 and showed that the disease will be eradicated from the system if R0
       
  • Coexistence of the solitary and periodic waves in convecting shallow water
           fluid
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Xianbo Sun, Wentao Huang, Junning CaiAbstractThe existence of a solitary wave for the shallow water model in convecting circumstance was established in previous works. It is still unknown that whether there exist periodic waves. In this paper, we prove that the models possess periodic waves with a fixed range of wave speed. The amplitude and wave speed are explicitly given. Moreover, the coexistence of the solitary wave and one periodic wave is established.
       
  • Global regularity of 2D generalized MHD equations with magnetic damping
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Caochuan Ma, Zhaoyun ZhangAbstractIn this paper, we focus on the global regularity of 2D generalized magnetohydrodynamics equations with magnetic damping b β−1b. Basing on the Maximal regularity of parabolic equation, we are able to show that this system has global smooth solutions when the initial data is sufficiently smooth.
       
  • Stationary solutions to outflow problem for 1-D compressible fluid models
           of Korteweg type: Existence, stability and convergence rate
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hakho HongAbstractIn this paper, we are concerned with the outflow problem in the half line (0,∞) to the isothermal compressible Navier–Stokes–Korteweg system with a nonlinear boundary condition for vanishing capillary tensor at x=0. We first give some necessary and sufficient conditions for the existence of the stationary solutions with the aid of center manifold theory. We also show the stability of the stationary solutions under smallness assumptions on the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solutions is obtained, provided that the initial perturbations belong to the weighted Sobolev spaces.
       
  • Dynamics of a waterborne pathogen model with spatial heterogeneity and
           general incidence rate
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yu Yang, Lan Zou, Jinling Zhou, Cheng-Hsiung HsuAbstractThis paper is concerned with the dynamics of a waterborne pathogen model with spatial heterogeneity and general incidence rate. We first establish the well-posedness of this model. Then we clarify the relationship between the local basic reproduction number R̃ and the basic reproduction number R0. It could be seen that R0 plays an important role in determining the global dynamics of this model. In fact, we show that the disease-free equilibrium is globally asymptotically stable when R01. We also consider the local and global stability of endemic equilibrium when all the parameters of this model are constant. In the case R0>1, we further establish the existence of traveling wave solutions of this model. Moreover, we provide an example and numerical simulations to support our theoretical results. Our model extended some known results.
       
  • Concentration and cavitation phenomena of Riemann solutions for the
           isentropic Euler system with the logarithmic equation of state
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Meina SunAbstractThe analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation.
       
  • Global stability of rarefaction waves for a viscous radiative and reactive
           gas with temperature-dependent viscosity
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yongkai LiaoAbstractWe study the nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional viscous radiative and reactive gas when the viscosity and heat conductivity coefficients depend on both density and absolute temperature. Our main idea is to use the smallness of the strength of the rarefaction waves to control the possible growth of its solutions induced by the nonlinearity of the system and the interactions of rarefaction waves from different families. The proof is based on some detailed analysis on uniform positive lower and upper bounds of the specific volume and the absolute temperature.
       
  • A free boundary tumor model with time dependent nutritional supply
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Wenlong Sun, Tomás Caraballo, Xiaoying Han, Peter E. KloedenAbstractA non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equation describing the evolution of the tumor size. First the global existence and uniqueness of a transient solution is established under some general conditions. Then with additional regularity assumptions on the consumption and proliferation rates, the existence and uniqueness of steady-state solutions is obtained. Furthermore the convergence of the transient solutions toward the steady-state solution is verified. Finally the long time behavior of the solutions is investigated by transforming the time-dependent domain to a fixed domain.
       
  • The global existence and asymptotic stability of solutions for a
           reaction–diffusion system
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Samir Bendoukha, Salem Abdelmalek, Mokhtar KiraneAbstractThis paper studies the solutions of a reaction–diffusion system with nonlinearities that generalize the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the solutions. Furthermore, we present some numerical examples.
       
  • Modeling eating disorders in young people
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Andrea Giacobbe, Giuseppe Mulone, Wendi WangAbstractA mathematical model is proposed to simulate the eating disorders of bulimia or anorexia. Earlier models are extended to incorporate the body mass index, which plays a key role in the eating attitude of self thinners. The global existence and ultimate boundedness of solutions of the nonlocal model are proved by using estimates of solutions. The basic reproduction number of eating disorder contagion is shown to be the invasion threshold. The testable linear and nonlinear stability conditions are established by Lyapunov functions. Further numerical simulations are given to reveal how self-forces and peer pressures to be thinner affect the emergence and distributions of eating disorders.
       
  • Invariant manifolds of Competitive Selection–Recombination dynamics
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Stephen Baigent, Belgin SeymenoğluAbstractWe study the two-locus-two-allele (TLTA) Selection–Recombination model from population genetics and establish explicit bounds on the TLTA model parameters for an invariant manifold to exist. Our method for proving existence of the invariant manifold relies on two key ingredients: (i) monotone systems theory (backwards in time) and (ii) a phase space volume that decreases under the model dynamics. To demonstrate our results we consider the effect of a modifier gene β on a primary locus α and derive easily testable conditions for the existence of the invariant manifold.
       
  • On the global dynamics and integrability of the Chemostat system
    • Abstract: Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Y. Paulina Martínez, Claudia VallsAbstractWe study a Chemostat system of the form ẋ=−qx+R̃K+yxy,ẏ=(c̃−y)q−R̃ã(K+y)xy,where q>0, R̃>0, K>0, c̃>0 and ã≠0. This system appears in competition modelling in biology. We describe its global dynamics on the Poincaré disc and study its Liouvillian integrability. For the first topic we use the well-known Poincaré compactification theory and for the second one we make use of the Puiseux series to derive the structure of all the irreducible invariant algebraic curves.
       
 
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