AM  Vol.6 No.10 , September 2015
Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains
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.

Cite this paper
Ahmed, E. , Abdelmajid, A. , Xu, L. and Ma, Q. (2015) Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains. Applied Mathematics, 6, 1790-1807. doi: 10.4236/am.2015.610159.
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