Limiting dynamics for stochastic nonclassical diffusion equations
نویسندگان
چکیده
<p style='text-indent:20px;'>In this paper, we are concerned with the dynamical behavior of stochastic nonclassical parabolic equation, more precisely, it is shown that inviscid limits diffusion equations reduces to heat equations. The key points in proof our convergence results establishing some uniform estimates and regularity theory for solutions which independent parameter. Based on estimates, tightness distributions can be obtained.</p>
منابع مشابه
Limiting dynamics for stochastic wave equations
In this paper, relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered. By introducing almost surely D–α-contracting property for random dynamical systems, we obtain a global random attractor of the stochastic wave equation νutt + ut − uν + f (uν) = √ νẆ endowed with Dirichlet boundary condition for any 0 < ν 1. The upper semicontinuity of thi...
متن کاملPullback Attractors for Nonclassical Diffusion Equations in Noncylindrical Domains
The existence and uniqueness of a variational solution are proved for the following nonautonomous nonclassical diffusion equation ut − εΔut − Δu f u g x, t , ε ∈ 0, 1 , in a noncylindrical domain with homogeneous Dirichlet boundary conditions, under the assumption that the spatial domains are bounded and increase with time. Moreover, the nonautonomous dynamical system generated by this class of...
متن کاملUniform Attractors for Non-autonomous Nonclassical Diffusion Equations on R
where ε ∈ [0, 1], the nonlinearity f and the external force g satisfy some certain conditions specified later. This equation is known as the nonclassical diffusion equation when ε > 0, and the reaction-diffusion equation when ε = 0. Nonclassical diffusion equation arises as a model to describe physical phenomena, such as non-Newtonian flows, soil mechanic, and heat conduction (see, e.g., [1, 7,...
متن کاملApproximation of stochastic advection diffusion equations with finite difference scheme
In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...
متن کاملDYNAMICS OF NON - AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON R n Cung
We consider the Cauchy problem for a non-autonomous nonclassical diffusion equation of the form ut − ε∆ut −∆u+ f(u) + λu = g(t) on Rn. Under an arbitrary polynomial growth order of the nonlinearity f and a suitable exponent growth of the external force g, using the method of tail-estimates and the asymptotic a priori estimate method, we prove the existence of an (H1(Rn) ∩ Lp(Rn), H1(Rn) ∩ Lp(Rn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B
سال: 2022
ISSN: ['1531-3492', '1553-524X']
DOI: https://doi.org/10.3934/dcdsb.2021288