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Attractors for damped hyperbolic equations on arbitrary unbounded domains

Martino Prizzi·Krzysztof P. Rybakowski
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Abstract

We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+α(x) u_t+β(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in Ω, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial Ω, t\in[,\infty[.\endaligned$$ on an unbounded domain $Ω$, without smoothness assumptions on $β(\cdot)$, $a_{ij}(\cdot)$, $f(\cdot,u)$ and $\partialΩ$, and $f(x,\cdot)$ having critical or subcritical growth.

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Martino Prizzi, Krzysztof P. Rybakowski. 2007-02-12. Attractors for damped hyperbolic equations on arbitrary unbounded domains. https://arxiv.org/abs/math/0601319

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