Random attractor of stochastic partly dissipative systems perturbed by Lévy noise

Jianhua Huang

doi:10.1186/1029-242x-2012-132

Abstract

The current paper is devoted to random dynamics of stochastic partly dissipative systems perturbed by Levy noise. By the technique of dissipative in probability and multivalued random dynamical systems (MRDS), the existences of random attractor for MRDS generated by the stochastically perturbed partly dissipative systems are provided, both the weaker restrictions and stronger restrictions on the coefficients of Levy noise respectively. Mathematics Subject Classification: 35R60; 60H15; 35K57.

Highlights

Global attractors play an important role in the study of asymptotic behavior of various nonlinear systems
Stochastic differential equations driven by Lévy processes have been summarized in [8]
Peszat and Zabczyk [9] have presented a basic framework for partial differential equations driven by Lévy processes, which extended several results known for stochastic partial differential equations (SPDEs) driven by Wiener processes

Summary

Introduction

Global attractors play an important role in the study of asymptotic behavior of various nonlinear systems. Kapustyan et al [10] follows the idea of the one in [6], and study the random attractor of reaction diffusion systems perturbed by càdlàg process. The author in [13] study the stochastic partly FitzHugh-Nagumo systems driven by Gaussian white noise, and show the existence of random attractor by uniform estimates on solution for large space and time variable via a cut-off technique.

Results

Conclusion