Attractors for reaction-diffusion equations on arbitrary unbounded domains

Abstract

We prove existence of global attractors for parabolic
equations of the form
$$
\alignedat2
u_t+\beta(x)u-
\sum_{ij}\partial_i(a_{ij}(x)\partial_j u)&=f(x,u),&\quad &x\in
\Omega,\ t\in[0,\infty[,\\
u(x,t)&=0,&\quad &x\in \partial \Omega,\ t\in[0,\infty[.
\endalignedat
$$
on an arbitrary unbounded domain $\Omega$ in $\mathbb R^3$, without
smoothness assumptions on $a_{ij}(\cdot)$ and $\partial\Omega$.