Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation
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 equa...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03212067 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |