Limiting dynamics for stochastic delay p-Laplacian equation on unbounded thin domains

Abstract

We study the long-term behavior of solutions for stochastic delay p-Laplacian equation with multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of tempered random attractors for these equations defined on \((n+1)\)-dimensional unbounded thin domains. Then, the upper semicontinuity 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.