Attractors for reaction-diffusion equations on arbitrary unbounded domains

Abstract

We prove existence of global attractors for parabolic equations of the form $$ \begin{alignedat}{2} u_t+\beta(x)u- \sum_{ij}\partial_i(a_{ij}(x)\partial_j u)&=f(x,u),&\quad &x\in \Omega,\ t\in[0,\infty[,\\ u(x,t)&=0,&\quad &x\in \partial \Omega,\ t\in[0,\infty[, \end{alignedat} $$ on an arbitrary unbounded domain $\Omega$ in $\mathbb R^3$, without smoothness assumptions on $a_{ij}(\cdot)$ and $\partial\Omega$.