Topological Methods in Nonlinear Analysis

Attractors for semilinear damped wave equations on arbitrary unbounded domains

Martino Prizzi and Krzysztof P. Rybakowski

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Abstract

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

Article information

Source
Topol. Methods Nonlinear Anal., Volume 31, Number 1 (2008), 49-82.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463150123

Mathematical Reviews number (MathSciNet)
MR2420655

Zentralblatt MATH identifier
1157.35321

Citation

Prizzi, Martino; Rybakowski, Krzysztof P. Attractors for semilinear damped wave equations on arbitrary unbounded domains. Topol. Methods Nonlinear Anal. 31 (2008), no. 1, 49--82. https://projecteuclid.org/euclid.tmna/1463150123


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