The aim of this paper is to study the long-time dynamics solutions evolution system { u t ? ? + ? ( ) 1 2 a ? v = f , x ? ? × ? ? 0 subject boundary conditions ? where bounded smooth domain in R n ? 3 with ?? assumed be regular enough, > constant, Hölder continuous function and dissipative nonlinearity. This problem non-autonomous version well known Klein-Gordon-Zakharov system. Using uniform s...

<p style='text-indent:20px;'>We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with driving noises Hölder continuity. Such systems can be solved Lyons' theory paths, in particular integrals are understood Gubinelli sense for controlled paths. Using framework random dynamical and attractors, we prove existence upper semi-continuity global pul...

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise. The considered are driven by discrete Laplacian, which features infinite-range interactions. We first prove existence pullback random attractor in <inline-formula><tex-math id="M1">\begin{document}$ \ell^2 $\end{documen...

<p style='text-indent:20px;'>A mathematical model describing the growth of gut microbiome inside and on wall is developed based chemostat with growth. Both concentration flow rate nutrient input are time-dependent, which results in a system non-autonomous differential equations. First stability each meaningful equilibrium studied for autonomous counterpart. Then existence pullback attract...

<p style='text-indent:20px;'>The global well-posedness and long-time mean random dynamics are studied for a high-dimensional non-autonomous stochastic nonlinear lattice pseudo-parabolic equation with <i>locally</i> Lipschitz drift diffusion terms. The existence uniqueness of three different types weak pullback attractors as well their relations established the dynamical system...