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Publisher: Springer-Verlag (Total: 2350 journals)

 Acta Applicandae Mathematicae   [SJR: 0.624]   [H-I: 34]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 0167-8019 - ISSN (Online) 1572-9036    Published by Springer-Verlag  [2350 journals]
• Uniqueness Result for Long Range Spatially Segregation Elliptic System
• Authors: Farid Bozorgnia
Pages: 1 - 14
Abstract: We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. We prove the uniqueness result for positive solution of those elliptic and related parabolic systems when the coupling in the right hand side involves a non-local term of integral form. Moreover, alternate proofs of some known results, such as existence of solutions in the elliptic case and the limiting configuration are given. The free boundary condition in a particular setting is given.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0129-y
Issue No: Vol. 154, No. 1 (2018)

• Gevrey Smoothness of Families of Invariant Curves for Analytic Area
Preserving Mappings
• Authors: Dongfeng Zhang; Junxiang Xu
Pages: 31 - 42
Abstract: In this paper we prove the existence of a Gevrey family of invariant curves for analytic area preserving mappings. The Gevrey smoothness is expressed by Gevrey index. We specifically obtain the Gevrey index of families of invariant curves which is related to the smoothness of area preserving mappings and the exponent of small divisors condition. Moreover, we obtain a Gevrey normal form of area preserving mappings in a neighborhood of the union of the invariant curves.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0131-4
Issue No: Vol. 154, No. 1 (2018)

• Mathematical Analysis of an Approximation Model for a Spherical Cloud of
Cavitation Bubbles
• Authors: Rostislav Vodák; Pavel Ženčák
Pages: 43 - 57
Abstract: In the paper we introduce a new approximation scheme for modelling a spherical cloud of cavitation bubbles based upon a model developed in (Wang and Brennen in J. Fluids Eng. 121(4):872–880, 1999) which consists of fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for dynamics of the bubbles. We prove existence of a unique, local-in-time solution to the equations using the Banach fixed-point theorem which also provides us with the convergent scheme for a numerical simulation of the solution. We further demonstrate acquired numerical results.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0132-3
Issue No: Vol. 154, No. 1 (2018)

• Finite-Band Solutions for the Hierarchy of Coupled Toda Lattices
• Authors: Xin Zeng; Xianguo Geng
Pages: 59 - 81
Abstract: Based on the characteristic polynomial of Lax matrix for the hierarchy of coupled Toda lattices associated with a $$3\times3$$ discrete matrix spectral problem, we introduce a trigonal curve with two infinite points, from which we establish the associated Dubrovin-type equations. The asymptotic properties of the meromorphic function and the Baker-Akhiezer function are studied near two infinite points on the trigonal curve. Finite-band solutions of the entire hierarchy of coupled Toda lattices are obtained in terms of the Riemann theta function.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0133-2
Issue No: Vol. 154, No. 1 (2018)

• Persistence of Besov Regularity for a Generalized Drift-Diffusion Equation
with Pressure
• Authors: Weiren Zhao
Pages: 83 - 93
Abstract: In this paper, we prove that Besov regularity of the initial data can persist for a generalized drift-diffusion equation with pressure under a very weak condition on the drift velocity. In particular, the solution is Hölder continuous.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0134-1
Issue No: Vol. 154, No. 1 (2018)

• Spatial Decay for Solutions to 2-D Boussinesq System with Variable Thermal
Diffusivity
• Authors: Yuanfei Li; Changhao Lin
Pages: 111 - 130
Abstract: In this paper, the authors derive an explicit spatial decay estimate for the time dependent flow of Boussinesq fluid with thermal conductivity depending on the temperature in a semi-infinite strip. By introducing a stream function, the authors established a decay estimate for an expression involving the stream function. To make the result explicit, an upper bound for total energy is also obtained. The results of this paper may be thought of as a version of Saint-Venant’s principle.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0136-z
Issue No: Vol. 154, No. 1 (2018)

• General Decay for a Viscoelastic Equation of Variable Coefficients in the
Presence of Past History with Delay Term in the Boundary Feedback and
Acoustic Boundary Conditions
• Authors: Yamna Boukhatem; Benyattou Benabderrahmane
Pages: 131 - 152
Abstract: In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function $$g$$ . Our result extends the decay result obtained for problems with finite history to those with infinite history.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0137-y
Issue No: Vol. 154, No. 1 (2018)

• Absolute Cesàro Series Spaces and Matrix Operators
• Authors: G. Canan Hazar; M. Ali Sarıgöl
Pages: 153 - 165
Abstract: In this paper we derive a series space $$\vert C_{\lambda,\mu} \vert _{k}$$ using the well known absolute Cesàro summability $$\vert C_{\lambda,\mu} \vert _{k}$$ of Das (Proc. Camb. Philol. Soc. 67:321–326, 1970), compute its $$\beta$$ -dual, give some algebraic and topological properties, and characterize some matrix operators defined on that space. So we generalize some results of Bosanquet (J. Lond. Math. Soc. 20:39–48, 1945), Flett (Proc. Lond. Math. Soc. 7:113–141, 1957), Mehdi (Proc. Lond. Math. Soc. (3)10:180–199, 1960), Mazhar (Tohoku Math. J. 23:433–451, 1971), Orhan and Sarıgöl (Rocky Mt. J. Math. 23(3):1091–1097, 1993) and Sarıgöl (Commun. Math. Appl. 7(1):11–22, 2016; Math. Comput. Model. 55:1763–1769, 2012).
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0138-x
Issue No: Vol. 154, No. 1 (2018)

• Weighted Hardy Type Spaces Estimates of Multilinear Singular Integral
Operators for the Extreme Cases
• Authors: Dazhao Chen
Pages: 167 - 187
Abstract: We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0139-9
Issue No: Vol. 154, No. 1 (2018)

• Quadratic Hamilton–Poisson Systems on se ( 1 , 1 ) − ∗
$\mathfrak{se}(1,1)^{*}_{-}$ : The Inhomogeneous Case
• Authors: D. I. Barrett; R. Biggs; C. C. Remsing
Pages: 189 - 230
Abstract: We consider equivalence, stability and integration of quadratic Hamilton–Poisson systems on the semi-Euclidean Lie–Poisson space $$\mathfrak{se}(1,1)^{*}_{-}$$ . The inhomogeneous positive semidefinite systems are classified (up to affine isomorphism); there are 16 normal forms. For each normal form, we compute the symmetry group and determine the Lyapunov stability nature of the equilibria. Explicit expressions for the integral curves of a subclass of the systems are found. Finally, we identify several basic invariants of quadratic Hamilton–Poisson systems.
PubDate: 2018-04-01
DOI: 10.1007/s10440-017-0140-3
Issue No: Vol. 154, No. 1 (2018)

• Weak Type Estimates of the Fractional Integral Operators on Morrey Spaces
with Variable Exponents
• Authors: Kwok-Pun Ho
Abstract: We show that when the infimum of the exponent function equals to 1, the fractional integral operator is a bounded operator from the Morrey space with variable exponent to the weak Morrey space with variable exponent.
PubDate: 2018-04-26
DOI: 10.1007/s10440-018-0181-2

• Computing Optimal Distances to Pareto Sets of Multi-Objective Optimization
Problems in Asymmetric Normed Lattices
• Authors: X. Blasco; G. Reynoso-Meza; E. A. Sánchez-Pérez; J. V. Sánchez-Pérez
Abstract: Given a finite dimensional asymmetric normed lattice, we provide explicit formulae for the optimization of the associated (non-Hausdorff) asymmetric “distance” among a subset and a point. Our analysis has its roots and finds its applications in the current development of effective algorithms for multi-objective optimization programs. We are interested in providing the fundamental theoretical results for the associated convex analysis, fixing in this way the framework for this new optimization tool. The fact that the associated topology is not Hausdorff forces us to define a new setting and to use a new point of view for this analysis. Existence and uniqueness theorems for this optimization are shown. Our main result is the translation of the original abstract optimal distance problem to a clear optimization scheme. Actually, this justifies the algorithms and shows new aspects of the numerical and computational methods that have been already used in visualization of multi-objective optimization problems.
PubDate: 2018-04-26
DOI: 10.1007/s10440-018-0184-z

• Authors: Rasul Ganikhodzhaev; Farrukh Mukhamedov; Mansoor Saburov
Abstract: The paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method for stable solutions is also presented.
PubDate: 2018-04-26
DOI: 10.1007/s10440-018-0183-0

• Nonlinear Elliptic Equations Without Sign Condition and L 1 $L^{1}$ -Data
in Musielak-Orlicz-Sobolev Spaces
• Authors: Mostafa El Moumni
Abstract: In this research we give the existence of solutions to a elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on ℝ. Not also that for right hand side, it is assumed that to be merely integrable. This results in formulation of the problem in Musielak-Orlicz-Sobolev spaces.
PubDate: 2018-04-26
DOI: 10.1007/s10440-018-0186-x

• Bernstein Fractal Trigonometric Approximation
• Authors: N. Vijender
Abstract: Fractal interpolation and approximation received a lot of attention in the last thirty years. The main aim of the current article is to study a fractal trigonometric approximants which converge to the given continuous function even if the magnitude of the scaling factors does not approach zero. In this paper, we first introduce a new class of fractal approximants, namely, Bernstein $$\alpha$$ -fractal functions using the theory of fractal approximation and Bernstein polynomial. Using the proposed class of fractal approximants and imposing no condition on corresponding scaling factors, we establish that the set of Bernstein $$\alpha$$ -fractal trigonometric functions is fundamental in the space of continuous periodic functions. Fractal version of Gauss formula of trigonometric interpolation is obtained by means of Bernstein trigonometric fractal polynomials. We study the Bernstein fractal Fourier series of a continuous periodic function $$f$$ defined on $$[-l,l]$$ . The Bernstein fractal Fourier series converges to $$f$$ even if the magnitude of the scaling factors does not approach zero. Existence of the $$\mathcal{C}^{r}$$ -Bernstein fractal functions is investigated, and Bernstein cubic spline fractal interpolation functions are proposed based on the theory of $$\mathcal{C}^{r}$$ -Bernstein fractal functions.
PubDate: 2018-04-24
DOI: 10.1007/s10440-018-0182-1

• Stability of the Equilibrium to the Vlasov-Poisson-Boltzmann System with
Non-constant Background Charge
• Authors: Xiuhui Yang; Xiujuan Li
Abstract: We study the global existence of classical solution to the Vlasov-Poisson-Boltzmann system with non-constant background charge. In this case the local Maxwellian is the unique stationary state. We show that this equilibrium is nonlinear stable provided that the initial perturbation is sufficient small. Our result solves an open problem stated by Duan and Yang (SIAM J. Math. Anal. 41(6):2353–2387, 2009) in one dimensional case.
PubDate: 2018-04-13
DOI: 10.1007/s10440-018-0176-z

• Global Existence and Asymptotic Behavior of Solutions to the Hyperbolic
Keller-Segel Equation with a Logistic Source
• Authors: Myeongju Chae
Abstract: In this paper we consider a hyperbolic Keller-Segel system with a logistic source in two dimension. We show the system has a global smooth solution upon small perturbation around a constant equilibrium and the solution satisfies a dissipative energy inequality. To do this we find a convex entropy functional and a compensating matrix, which transforms the partially dissipative system into a uniformly dissipative one. Those two ingredients were crucial for the study of a partially dissipative hyperbolic system (Hanouzet and Natalini in Arch. Ration. Mech. Anal. 169(2):89–117, 2003; Kawashima in Ph.D. Thesis, Kyoto University, 1983; Yong in Arch. Ration. Mech. Anal. 172(2):247–266, 2004).
PubDate: 2018-04-10
DOI: 10.1007/s10440-018-0180-3

• Global Well-posedness for the Density-Dependent Incompressible Flow of
Liquid Crystals
• Authors: Xiaoping Zhai; Zhi-Min Chen
Abstract: In the present paper, we consider the global well-posedness of the density-dependent incompressible flow of liquid crystals in $$\mathbb{R}^{2}$$ . The local existence and uniqueness of the system are obtained without the assumption of small density variation. The global well-posedness is proved when the initial density and liquid crystal orientation are small. However, the initial velocity field is allowed to be arbitrarily large.
PubDate: 2018-04-09
DOI: 10.1007/s10440-018-0178-x

• Markov Chain Approximation of Pure Jump Processes
• Authors: Ante Mimica; Nikola Sandrić; René L. Schilling
Abstract: In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a given Markov process by Markov chains.
PubDate: 2018-04-05
DOI: 10.1007/s10440-018-0179-9

• Subharmonic Solutions with Prescribed Minimal Period of a Forced Pendulum
Equation with Impulses
• Authors: Fanchao Kong
Abstract: This paper is mainly concerned with a forced pendulum equation with impulses and the length of the pendulum is variable. The main tool utilized to establish our results on the subharmonic solutions with prescribed minimal period is the theorem of the least action principle due to Mawhin and Willem. As an application, three examples are given, and the corresponding numerical subharmonic solutions for the examples are obtained by applying Matlab software. Some results in the literature can be generalized and improved.
PubDate: 2018-04-04
DOI: 10.1007/s10440-018-0177-y

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