Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 858152 | https://doi.org/10.1155/S1110757X03212067

Robert Willie, "Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation", Journal of Applied Mathematics, vol. 2003, Article ID 858152, 19 pages, 2003. https://doi.org/10.1155/S1110757X03212067

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

Received20 Dec 2002

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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