Random Attractor for the Nonclassical Diffusion Equation with Fading Memory

Random Attractor for the Nonclassical Diffusion Equation with Fading Memory

Year:    2015

Author:    Shuilin Cheng

Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 3 : pp. 253–268

Abstract

In this paper,we consider the stochastic nonclassical diffusion equationwith fading memory on a bounded domain. By decomposition of the solution operator, we give the necessary condition of asymptotic smoothness of the solution to the initial boundary value problem, and then we prove the existence of a random attractor in the space $M_1=D(A^{\frac{1}{2}}) × L^2_μ(R^+, D(A^{\frac{1}{2}}))$, where A=-Δ with Dirichlet boundary condition.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v28.n3.4

Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 3 : pp. 253–268

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Stochastic nonclassical diffusion equations

Author Details

Shuilin Cheng

  1. Asymptotic Behavior of Random Reaction-diffusion Delay Equations Driven by Colored Noise

    Ma, Wenjun | Ma, Qiaozhen

    Taiwanese Journal of Mathematics, Vol. 27 (2023), Iss. 4

    https://doi.org/10.11650/tjm/230301 [Citations: 0]
  2. Dynamics of fractional nonclassical diffusion equations with delay driven by additive noise on $ \mathbb{R}^n $

    Chen, Pengyu | Wang, Bixiang | Zhang, Xuping

    Discrete and Continuous Dynamical Systems - B, Vol. 27 (2022), Iss. 9 P.5129

    https://doi.org/10.3934/dcdsb.2021267 [Citations: 2]
  3. Uniform Attractors of Nonclassical Diffusion Equations Lacking Instantaneous Damping on $\mathbb{R}^{N}$ with Memory

    Toan, Nguyen Duong

    Acta Applicandae Mathematicae, Vol. 170 (2020), Iss. 1 P.789

    https://doi.org/10.1007/s10440-020-00359-1 [Citations: 8]
  4. Uniform attractors of nonclassical diffusion equations on ℝN with memory and singularly oscillating external forces

    Le, Thi Thuy | Nguyen, Duong Toan

    Mathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 1 P.820

    https://doi.org/10.1002/mma.6791 [Citations: 5]
  5. Long-time dynamics of fractional nonclassical diffusion equations with nonlinear colored noise and delay on unbounded domains

    Chen, Pengyu | Wang, Renhai | Zhang, Xuping

    Bulletin des Sciences Mathématiques, Vol. 173 (2021), Iss. P.103071

    https://doi.org/10.1016/j.bulsci.2021.103071 [Citations: 29]