Convergence of Random Attractors for Stochastic Delay p-Laplacian Equation Driven by Nonlinear Colored Noise on Unbounded Thin Domains

Abstract

We study the limiting behavior of solutions for stochastic delay p-Laplacian equation with nonlinear multiplicative colored noise on unbounded thin domains. There are three major ingredients. The first ingredient is to prove the existence and uniqueness of tempered random attractors for these equations. Secondly, the upper semi-continuity of these attractors when a family of \((n+1)\)-dimensional thin domains degenerates onto an n-dimensional domain as the thinness measure approaches zero is established. The final ingredient is to show the upper semi-continuity of these delay random attractors when the length of time delay tends to zero.