Authors:Jishan Fan; Fucai Li; Gen Nakamura Pages: 1 - 10 Abstract: Abstract This paper proves a regularity criterion for the \(3D\) full compressible Navier-Stokes-Maxwell system in a bounded domain. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0085-y Issue No:Vol. 149, No. 1 (2017)

Authors:Charline Smadi Pages: 11 - 51 Abstract: Abstract Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in the genetic signature left by a selective sweep induced by recurrent mutations at a given locus from an allele \(A\) to an allele \(a\) , depending on the mutation frequency. We distinguish three possible scales for the mutation probability per reproductive event, which entail distinct genetic signatures. Besides, we study the hydrodynamic limit of the \(A\) - and \(a\) -population size dynamics when mutations are frequent, and find non trivial equilibria leading to several possible patterns of polymorphism. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0086-x Issue No:Vol. 149, No. 1 (2017)

Authors:Alessandro Montino; Antonio DeSimone Pages: 53 - 86 Abstract: Abstract The three-sphere swimmer by Najafi and Golestanian is composed of three spheres connected by two arms. The case in which the swimmer can control the lengths of the two arms has been studied in detail. Here we study a variation of the model in which the swimmer’s arms are constructed according to Hill’s model of muscular contraction. The swimmer is able to control the tension developed in the active components of the arms. The two shape parameters and the tensions acting on the two arms are then obtained by solving a system of ordinary differential equations. We study the qualitative properties of the solutions, compute analytically their leading order approximation and compare them with numerical simulations. We also formulate and solve some optimisation problems, aimed at finding the actuation strategies maximising performance, for various performance measures. Finally, we discuss the structure of the governing equations of our microswimmers from the point of view of control theory. We show that our systems are control affine systems with drift. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0087-9 Issue No:Vol. 149, No. 1 (2017)

Authors:Mohammad F. Al-Jamal Pages: 87 - 99 Abstract: Abstract We consider the inverse problem of reconstructing the initial condition of a one-dimensional time-fractional diffusion equation from measurements collected at a single interior location over a finite time-interval. The method relies on the eigenfunction expansion of the forward solution in conjunction with a Tikhonov regularization scheme to control the instability inherent in the problem. We show that the inverse problem has a unique solution provided exact data is given, and prove stability results regarding the regularized solution. Numerical realization of the method and illustrations using a finite-element discretization are given at the end of this paper. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0088-8 Issue No:Vol. 149, No. 1 (2017)

Authors:Changwook Yoon; Yong-Jung Kim Pages: 101 - 123 Abstract: Abstract The global existence and the instability of constant steady states are obtained together for a Keller-Segel type chemotactic aggregation model. Organisms are assumed to change their motility depending only on the chemical density but not on its gradient. However, the resulting model is closely related to the logarithmic model, $$\begin{aligned} u_{t}=\Delta \bigl(\gamma (v)u\bigr)=\nabla \cdot \biggl(\gamma (v) \biggl(\nabla u- \frac{k}{v}u\nabla v \biggr) \biggr),\quad v_{t}={\varepsilon }\Delta v-v+u, \end{aligned}$$ where \(\gamma (v):=c_{0}v^{-k}\) is the motility function. The global existence is shown for all chemosensitivity constant \(k>0\) with a smallness assumption on \(c_{0}>0\) . On the other hand constant steady states are shown to be unstable only if \(k>1\) and \({\varepsilon }>0\) is small. Furthermore, the threshold diffusivity \({\varepsilon }_{1}>0\) is found that, if \({\varepsilon }<{\varepsilon }_{1}\) , any constant steady state is unstable and an aggregation pattern appears. Numerical simulations are given for radial cases. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0089-7 Issue No:Vol. 149, No. 1 (2017)

Authors:Eduardo Hernández; Donal O’Regan Pages: 125 - 137 Abstract: In this paper we introduce a new class of abstract integro-differential equations with delay and we study the existence of strict solutions. An application involving the heat equation with memory is presented. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0090-1 Issue No:Vol. 149, No. 1 (2017)

Authors:Zujin Zhang Pages: 139 - 144 Abstract: Abstract This paper studies the 3D generalized MHD system with fractional diffusion terms \((-\triangle)^{\alpha}\boldsymbol{u}\) and \((-\triangle )^{\beta}\boldsymbol{b}\) with \(0<\alpha<\frac{5}{4}\leq\beta\) , and establishes a regularity criterion involving the velocity gradient in Besov spaces of negative order. This improves Fan et al. (Math. Phys. Anal. Geom. 17:333–340, 2014) a lot. PubDate: 2017-06-01 DOI: 10.1007/s10440-016-0091-0 Issue No:Vol. 149, No. 1 (2017)

Authors:Rory Biggs; Claudiu C. Remsing Pages: 1 - 59 Abstract: Abstract Quadratic Hamilton–Poisson systems on three-dimensional Lie–Poisson spaces are considered. The homogeneous (positive) semidefinite systems are classified up to linear isomorphism; an exhaustive and nonredundant list of 23 normal forms is exhibited. For each normal form, the stability nature of the equilibria is determined. Each normal form is explicitly integrated, with the exception of three families of systems. Based on the analysis of the normal forms, some simple invariants are identified. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0074-1 Issue No:Vol. 148, No. 1 (2017)

Authors:Xia Ye Pages: 61 - 69 Abstract: Abstract In this paper, we consider the Cauchy problem of non-stationary motion of heat-conducting incompressible viscous fluids in \(\mathbb{R}^{2}\) , where the viscosity and heat-conductivity coefficient vary with the temperature. It is shown that the Cauchy problem has a unique global-in-time strong solution \((u, \theta)(x,t)\) on \(\mathbb{R}^{2}\times(0,\infty)\) , provided the initial norm \(\ \nabla u_{0}\ _{L^{2}}\) is suitably small, or the lower-bound of the coefficient of heat conductivity (i.e. \(\underline{\kappa}\) ) is large enough, or the derivative of viscosity (i.e. \( \mu'(\theta) \) ) is small enough. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0078-x Issue No:Vol. 148, No. 1 (2017)

Authors:Onur Gün; Atilla Yilmaz Pages: 71 - 102 Abstract: Abstract We propose a new model of permanent monogamous pair formation in zoological populations with multiple types of females and males. According to this model, animals randomly encounter members of the opposite sex at their so-called firing times to form temporary pairs which then become permanent if mating happens. Given the distributions of the firing times and the mating preferences upon encounter, we analyze the contingency table of permanent pair types in three cases: (i) definite mating upon encounter; (ii) Poisson firing times; and (iii) Bernoulli firing times. In the first case, the contingency table has a multiple hypergeometric distribution which implies panmixia. The other two cases generalize the encounter-mating models of Gimelfarb (Am. Nat. 131(6):865–884, 1988) who gives conditions that he conjectures to be sufficient for panmixia. We formulate adaptations of his conditions and prove that they not only characterize panmixia but also allow us to reduce the model to the first case by changing its underlying parameters. Finally, when there are only two types of females and males, we provide a full characterization of panmixia, homogamy and heterogamy. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0079-9 Issue No:Vol. 148, No. 1 (2017)

Authors:Hongling Jiang; Lijuan Wang Pages: 103 - 120 Abstract: Abstract This paper is concerned with a Variable-territory model with limited self-limitation of predator. By the bifurcation theorem, regular perturbation theorem and numerical simulation, the conditions of existence, stability and convergence of positive solutions are established. This work shows that prey and predator can be controlled by parameters in Variable-territory model, such as intrinsic growth rate, death rate, handling time and the self-limitation of predator. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0080-3 Issue No:Vol. 148, No. 1 (2017)

Authors:Ling Zhou; Shan Zhang; Zuhan Liu Pages: 121 - 142 Abstract: Abstract In this paper we consider the system of reaction-diffusion-advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. In strong competition case, we study the influence of competition rates on the long time behavior of solutions and prove that two species spatially segregate as the competition rates become large. Besides, by using a blow up method, we obtain the uniform Hölder bounds for solutions of the system. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0081-2 Issue No:Vol. 148, No. 1 (2017)

Authors:Tuan Nguyen Huy; Mokhtar Kirane; Bessem Samet; Van Au Vo Pages: 143 - 155 Abstract: Abstract We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement. PubDate: 2017-04-01 DOI: 10.1007/s10440-016-0082-1 Issue No:Vol. 148, No. 1 (2017)

Authors:Balázs Boros; Josef Hofbauer; Stefan Müller Abstract: Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particular, we characterize its global asymptotic stability in terms of the kinetic orders. PubDate: 2017-05-23 DOI: 10.1007/s10440-017-0102-9

Authors:Roberto Castelli Abstract: In this paper a method to rigorously compute several non trivial solutions of the Gray-Scott reaction-diffusion system defined on a 2-dimensional bounded domain is presented. It is proved existence, within rigorous bounds, of non uniform patterns significantly far from being a perturbation of the homogenous states. As a result, a non local diagram of families that bifurcate from the homogenous states is depicted, also showing coexistence of multiple solutions at the same parameter values. Combining analytical estimates and rigorous computations, the solutions are sought as fixed points of a operator in a suitable Banach space. To address the curse of dimensionality, a variation of the existing technique is presented, necessary to enable successful computations in reasonable time. PubDate: 2017-05-22 DOI: 10.1007/s10440-017-0101-x

Authors:M. L. Santos; A. D. S. Campelo; D. S. Almeida Júnior Abstract: In this work we are considering the porous elastic system with porous elastic dissipation and with elastic dissipation. Our main result is to show that the corresponding semigroup is exponentially stable if and only if the wave speeds of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal. It is worth noting that the result obtained here is different from all existing in the literature for porous elastic materials, where the sum of the two slow decay processes determine a process that decay exponentially. Numerical experiments using finite differences are given to confirm our analytical results. Our numerical results are qualitatively in agreement with the corresponding results from dynamical in infinite dimensional. PubDate: 2017-05-19 DOI: 10.1007/s10440-017-0100-y

Authors:Gergő Nemes Abstract: In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also give re-expansions for these remainder terms and provide their error estimates. A detailed discussion on the sharpness of our error bounds and their relation to other results in the literature is given. The techniques used in this paper should also generalize to asymptotic expansions which arise from an application of the method of steepest descents. PubDate: 2017-05-17 DOI: 10.1007/s10440-017-0099-0

Authors:A. Ambrazevičius; V. Skakauskas Abstract: Abstract Coupled system of nonlinear parabolic equations for grain drying is proposed and the existence and uniqueness theorem of classical solutions is proved by using the upper and lower solutions technique. The long-time behaviour of the solution is also investigated. PubDate: 2017-05-15 DOI: 10.1007/s10440-017-0098-1

Authors:Xinghong Pan Abstract: Abstract In this paper, we study the regularity of 3d axisymmetric Navier-Stokes equations under a prior point assumption on \(v^{r}\) or \(v^{z}\) . That is, the weak solution of the 3d axisymmetric Navier-Stokes equations \(v\) is smooth if $$ rv^{r}\geq-1; \quad\mbox{or}\quad r\bigl v^{r}(t,x)\bigr \leq Cr^{\alpha}, \ \alpha\in(0,1];\quad\mbox{or} \quad r\bigl v^{z}(t,x)\bigr \leq Cr^{ \beta},\ \beta\in[0,1]; $$ where \(r\) is the distance from the point \(x\) to the symmetric axis. PubDate: 2017-04-06 DOI: 10.1007/s10440-017-0096-3

Authors:Jiayin Liu; Duchao Liu; Peihao Zhao Abstract: Abstract This paper is concerned with a kind of quasilinear Schrödinger equation with combined nonlinearities, a convex term with any growth and a singular term, in a bounded smooth domain. Multiplicity results are obtained by critical point theory together with truncation arguments and the method of upper and lower solutions. PubDate: 2016-12-21 DOI: 10.1007/s10440-016-0084-z