Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains

Eshag Mohamed Ahmed, Ali Dafallah Abdelmajid, Ling Xu, Qiaozhen Ma^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.

DOI: 10.4236/am.2015.610159                

Abstract

In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.

Keywords

Stochastic Reaction-Diffusion Equation, Random Attractors, Distribution Derivatives, Asymptotic Compactness, Unbounded Domain

Conflicts of Interest

The authors declare no conflicts of interest.

References

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