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2008 Attractors for semilinear damped wave equations on arbitrary unbounded domains
Martino Prizzi, Krzysztof P. Rybakowski
Topol. Methods Nonlinear Anal. 31(1): 49-82 (2008).

Abstract

We prove existence of global attractors for semilineardamped 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 $\Omega$, withoutsmoothness assumptions on $\beta(\cdot)$,$a_{ij}(\cdot)$, $f(\cdot,u)$ and$\partial\Omega$, and $f(x,\cdot)$ having critical or subcritical growth.

Citation

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Martino Prizzi. Krzysztof P. Rybakowski. "Attractors for semilinear damped wave equations on arbitrary unbounded domains." Topol. Methods Nonlinear Anal. 31 (1) 49 - 82, 2008.

Information

Published: 2008
First available in Project Euclid: 13 May 2016

zbMATH: 1157.35321
MathSciNet: MR2420655

Rights: Copyright © 2008 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.31 • No. 1 • 2008
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