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Random Attractor for the Nonclassical Diffusion Equation with Fading Memory

Random Attractor for the Nonclassical Diffusion Equation with Fading Memory
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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.

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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

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