Authors:Van-Sang Ngo Pages: 1 - 42 Abstract: In this article, we study an anisotropic rotating system arising in magnetohydrodynamics (MHD) in the whole space \(\mathbb{R}^{3}\) , in the case where there are no diffusivity in the vertical direction and a vanishing diffusivity in the horizontal direction (when the rotation goes to infinity). We first prove the local existence and uniqueness of a strong solution and then, using Strichartz-type estimates, we prove that this solution exists globally in time for large initial data, when the rotation is fast enough. PubDate: 2017-08-01 DOI: 10.1007/s10440-016-0092-z Issue No:Vol. 150, No. 1 (2017)

Authors:Bernard Ducomet; Marek Kobera; Šárka Nečasová Pages: 43 - 65 Abstract: We consider a simplified model based on the Navier-Stokes-Fourier system coupled to a transport equation and the Maxwell system, proposed to describe radiative flows in stars. We establish global-in-time existence for the associated initial-boundary value problem in the framework of weak solutions. PubDate: 2017-08-01 DOI: 10.1007/s10440-016-0093-y Issue No:Vol. 150, No. 1 (2017)

Authors:Fuyi Xu; Xinguang Zhang; Yonghong Wu; Lishan Liu Pages: 67 - 80 Abstract: The present paper is dedicated to the study of the Cauchy problems for the three-dimensional compressible nematic liquid crystal flow. We obtain the global existence and the optimal decay rates of smooth solutions to the system under the condition that the initial data in lower regular spaces are close to the constant equilibrium state. Our main method is based on the spectral analysis and the smooth effect of dissipative operator. PubDate: 2017-08-01 DOI: 10.1007/s10440-017-0094-5 Issue No:Vol. 150, No. 1 (2017)

Authors:J.-P. Antoine; M. Speckbacher; C. Trapani Pages: 81 - 101 Abstract: We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several examples, both discrete and continuous, are presented. PubDate: 2017-08-01 DOI: 10.1007/s10440-017-0095-4 Issue No:Vol. 150, No. 1 (2017)

Authors:Xinghong Pan Pages: 103 - 109 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: 2017-08-01 DOI: 10.1007/s10440-017-0096-3 Issue No:Vol. 150, No. 1 (2017)

Authors:Charline Smadi Pages: 11 - 51 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: 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: 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: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: 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:Silvia Bertoluzza; Valérie Perrier Abstract: In this article we introduce a new mixed Lagrange–Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a slight modification of the interpolating wavelets on the interval of Donoho, it leads to fast decomposition, error estimates and norm equivalences. This new basis is then used in adaptive wavelet collocation schemes for the solution of one dimensional fourth order problems. Numerical tests conducted on the 1D Euler–Bernoulli beam problem, show the efficiency of the method. PubDate: 2017-07-13 DOI: 10.1007/s10440-017-0110-9

Authors:Kuo-Shou Chiu Abstract: In this paper we introduce an impulsive cellular neural network models with piecewise alternately advanced and retarded argument. The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution. The approaches are based on employing Banach’s fixed point theorem and a new integral inequality of Gronwall type with impulses and deviating arguments. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides flexibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results. PubDate: 2017-06-16 DOI: 10.1007/s10440-017-0108-3

Authors:Lance Nielsen Abstract: We establish a comprehensive stability theory for Feynman’s operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported. PubDate: 2017-06-16 DOI: 10.1007/s10440-017-0109-2

Authors:Claudianor O. Alves; Ailton R. da Silva Abstract: The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems $$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon \nabla u \bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where \(\epsilon\) is a positive parameter, \(N\geq2\) , \(V\) , \(f\) are continuous functions satisfying some technical conditions and \(\phi\) is a \(C^{1}\) -function. PubDate: 2017-06-14 DOI: 10.1007/s10440-017-0107-4

Authors:Tong Tang; Hongjun Gao Abstract: In this paper, we study the compressible Euler-Korteweg equations with free boundary condition in vacuum. Under physically assumptions of positive density and pressure, we introduce some physically quantities to show that the spreading diameter of regions grows linearly in time. This is an interesting result as one would expect that the capillary forces would prevent the boundary from spreading. Moreover, we construct a spherically symmetric global solution to support our theorem, followed by Sideris (J. Differ. Equ. 257:1–14, 2014). PubDate: 2017-06-05 DOI: 10.1007/s10440-017-0097-2

Authors:Huiling Li; Yang Zhang Abstract: This paper concerns global existence and finite time blow-up behavior of positive solutions for a nonlinear reaction-diffusion system with different diffusion coefficients. By use of algebraic matrix theory and modern analytical theory, we extend results of Wang (Z. Angew. Math. Phys. 51:160–167, 2000) to a more general system. Furthermore, we give a complete answer to the open problem which was brought forward in Wang (Z. Angew. Math. Phys. 51:160–167, 2000). PubDate: 2017-06-05 DOI: 10.1007/s10440-017-0105-6

Authors:Cong Nhan Le; Xuan Truong Le Abstract: The main goal of this work is to study an initial boundary value problem for a quasilinear parabolic equation with logarithmic source term. By using the potential well method and a logarithmic Sobolev inequality, we obtain results of existence or nonexistence of global weak solutions. In addition, we also provided sufficient conditions for the large time decay of global weak solutions and for the finite time blow-up of weak solutions. PubDate: 2017-06-05 DOI: 10.1007/s10440-017-0106-5

Authors:Wolfgang Bock; Torben Fattler; Ludwig Streit Abstract: We prove that there exists a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion, \(\mu_{ {g,H}}\) , \(H\in (0,1)\) for \(dH < 1\) . The diffusion is constructed in the framework of Dirichlet forms in infinite dimensional (Gaussian) analysis. Moreover, the process is invariant under time translations. PubDate: 2017-06-01 DOI: 10.1007/s10440-017-0103-8

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: 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