Attractors for damped hyperbolic equations on arbitrary unbounded domains

Details Attractors for damped hyperbolic equations on arbitrary unbounded domains Attractors for damped hyperbolic equations on arbitrary unbounded domains

2006-01-13

arxiv.org/abs/math/0601319v3

Mathematics

Analysis of PDEs

34 pages; corrected typos

Scientific paper

We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+\alpha(x) u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in \Omega, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial \Omega, t\in[,\infty[.\endaligned$$ 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.

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