Attractors for semilinear damped wave equations on arbitrary unbounded domains

Martino Prizzi, Krzysztof P. Rybakowski

DOI: http://dx.doi.org/10.12775/TMNA.2008.004

Abstract


We prove existence of global attractors for semilinear
damped wave equations of the form
$$
\alignat 2
\eps u_{tt}+\alpha(x)
u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),
&\quad &x\in \Omega,t\in[0,\infty[,
\\
u(x,t)&=0,&\quad& x\in \partial \Omega,\ t\in[0,\infty[.
\endalignat
$$
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.

Keywords


Attractors; damped wave equations; unbounded domains; tail-estimates

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