Regularity of random attractors for stochastic reaction-diffusion equations on unbounded domains

2015/07/03 by Bao Quoc Tang
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · doi:10.1142/s0219493716500064

Abstract

The existence of a unique random attractors in [Formula: see text] for a stochastic reaction-diffusion equation with time-dependent external forces is proved. Due to the presence of both random and non-autonomous deterministic terms, we use a new theory of random attractors which is introduced in [B. Wang, J. Differential Equations 253 (2012) 1544–1583] instead of the usual one. The asymptotic compactness of solutions in [Formula: see text] is established by combining “tail estimate” technique and some new estimates on solutions. This work improves some recent results about the regularity of random attractors for stochastic reaction-diffusion equations.

Citations

• ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

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