Attractors for reaction-diffusion equations on arbitrary unbounded domains

Abstract

We prove existence of global attractors for parabolic equations of the form $$u_t+\beta (x)u-\sum _{ij}{\partial }_i(a_{ij}(x){\partial }_{j}u)=f(x,u)$$ with Dirichlet boundary condition on an arbitrary unbounded domain $\Omega$ in ${\mathbb{R}}^3$, without smoothness assumptions on $a_{ij}(\cdot )$ and $\partial \Omega$.

26 pages

References in corpus (1)

• Attractors for singularly perturbed hyperbolic equations on unbounded domains