Random dynamics for non-autonomous stochastic evolution equations without uniqueness on unbounded narrow domains

Abstract

Listen

Translate article

This paper deals with the limiting behavior of non-autonomous stochastic reaction-diffusion equations without uniqueness on unbounded narrow domains. We prove the existence and upper semicontinuity of random attractors for the equations on a family of unbounded (n + 1)-dimensional narrow domains, which collapses onto an n-dimensional domain. Since the solutions are non-uniqueness, which leads to a multivalued random dynamical system with the solution operators of the equation, we will prove the existence and upper semicontinuity of attractors by multivalued random dynamical system theory.