THE LONG TIME BEHAVIOR FOR PARTLY DISSIPATIVE STOCHASTIC SYSTEMS

Xianyun Du; Boling Guo

doi:10.11948/2011031

2011 Volume 1 Issue 4

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Xianyun Du, Boling Guo. THE LONG TIME BEHAVIOR FOR PARTLY DISSIPATIVE STOCHASTIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 449-465. doi: 10.11948/2011031

Citation:

Xianyun Du, Boling Guo. THE LONG TIME BEHAVIOR FOR PARTLY DISSIPATIVE STOCHASTIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 449-465. doi: 10.11948/2011031

THE LONG TIME BEHAVIOR FOR PARTLY DISSIPATIVE STOCHASTIC SYSTEMS

Xianyun Du¹,
Boling Guo²

1 College of mathematics, Chengdu university of information technology, Chengdu 610225, P. R. China;
2 Institute of applied physics and computational mathematics, P. O. Box 8009-28, 100088. P. R. China

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Abstract

Abstract

In this paper, we consider the long time behaviors for the partly dissipative stochastic reaction diffusion equations in D ⊂ Rⁿ. The main purpose of this paper is to establish the existence of a compact global random attractor. The existence of a random absorbing set is first discussed for the systems and then an estimate on the solutions is derived when the time is large enough, which ensures the asymptotic compactness of solutions. Finally, we establish the existence of the global attractor in L²(D)×L²(D).
- partly dissipative /
- random attractor /
- stochastic reaction-diffusion equation /
- asymptotic compactness
MSC: 35B40

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