Related papers: Exponential attractor for the viscoelastic wave mo…
In this paper, we consider global existence of classical solutions to the following kinetic model of pattern formation \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u)+\mu u(1-u) -\Delta v+v=u \end{cases} \qquad (0.1)…
We consider the 3D viscous primitive equations with periodic boundary conditions. These equations arise in the study of ocean dynamics and generate a dynamical system in a Sobolev H^1 type space. Our main result establishes the so-called…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…
Non-conformal attractor behavior is studied by solving non-conformal second order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and…
We consider a nonlinear (Berger or Von Karman) clamped plate model with a {\em piston-theoretic} right hand side---which include non-dissipative, non-conservative lower order terms. The model arises in aeroelasticity when a panel is…
In this paper, we study the following the coupled chemotaxis--haptotaxis model with remodeling of non-diffusible attractant $$ \left\{\begin{array}{ll} u_t = \Delta u-\chi\nabla\cdot(u\nabla v)- \xi\nabla\cdot(u\nabla w)+\mu u(1- u-w),…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the…
In this paper, we are concerned with the following viscoelastic wave equation \begin{equation*} \label{1} u_{tt}-\nabla u +\int_0^t g_1 (t-s)~ div(a_1(x) \nabla u(s))~ ds + \int_0^{+ \infty} g_2 (s)~ div(a_2(x) \nabla u(t-s)) ~ds = 0,…
The goal of the present paper is to study the asymptotic behavior of solutions for the viscoelastic wave equation with variable exponents \[ u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds+a|u_t|^{m(x)-2}u_t=b|u|^{p(x)-2}u\] under…
Dynamical system analysis of a universe model which contains matter, radiation, and quintessence with exponential potential, $V \!(\phi)=V_{\!o} \, exp(-\alpha \kappa \phi) \,$, is studied in the light of recent observations and the…
Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time-evolution to a non-thermal fixed point. We find universal dynamics connected with the occurrence of…
In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading…
We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these…
The manuscript considers the model for conversion of mechanical energy into heat during acoustic wave propagation in the presence of temperature-dependent elastic parameters, as given by \[ \left\{ \begin{array}{l} u_{tt} = (\gamma(\Theta)…
New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…