Attractors for damped hyperbolic equations on arbitrary unbounded domains

Abstract

We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+α(x) u_t+β(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in Ω, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial Ω, t\in[,\infty[.\endaligned$$ on an unbounded domain $\Omega$, without smoothness assumptions on $\beta (\cdot )$, $a_{ij}(\cdot )$, $f(\cdot ,u)$ and $\partial \Omega$, and $f(x,\cdot )$ having critical or subcritical growth.

34 pages; corrected typos

References in corpus (1)

• Attractors for singularly perturbed hyperbolic equations on unbounded domains

Cited by in corpus (3)

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• Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3
• Attractors for singularly perturbed hyperbolic equations on unbounded domains