Large diffusivity finite‐dimensional asymptotic behaviour of a semilinear wave equation

Robert Willie

Journal of Applied Mathematics, 2003, vol. 2003, issue 8, 409-427

Abstract: We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin‐type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second‐order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.

Date: 2003
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https://doi.org/10.1155/S1110757X03212067

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2003:y:2003:i:8:p:409-427

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