Attractors for semilinear damped wave equations on arbitrary unbounded domains
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Attractors, damped wave equations, unbounded domains, tail-estimatesAbstrakt
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.Pobrania
Opublikowane
2008-03-01
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PRIZZI, Martino & RYBAKOWSKI, Krzysztof P. Attractors for semilinear damped wave equations on arbitrary unbounded domains. Topological Methods in Nonlinear Analysis [online]. 1 marzec 2008, T. 31, nr 1, s. 49–82. [udostępniono 26.5.2024].
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