Attractors for semilinear damped wave equations on arbitrary unbounded domains
Keywords
Attractors, damped wave equations, unbounded domains, tail-estimatesAbstract
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.Downloads
Published
2008-03-01
How to Cite
1.
PRIZZI, Martino and RYBAKOWSKI, Krzysztof P. Attractors for semilinear damped wave equations on arbitrary unbounded domains. Topological Methods in Nonlinear Analysis. Online. 1 March 2008. Vol. 31, no. 1, pp. 49 - 82. [Accessed 24 April 2024].
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