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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832560373847293952 |
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| author | Robert Willie |
| author_facet | Robert Willie |
| author_sort | Robert Willie |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2e817ff2ff624c6e9b6df9155600a340 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2e817ff2ff624c6e9b6df9155600a3402025-02-03T01:27:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-012003840942710.1155/S1110757X03212067Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equationRobert Willie0Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid 28040, SpainWe 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.http://dx.doi.org/10.1155/S1110757X03212067 |
| spellingShingle | Robert Willie Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation Journal of Applied Mathematics |
| title | Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation |
| title_full | Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation |
| title_fullStr | Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation |
| title_full_unstemmed | Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation |
| title_short | Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation |
| title_sort | large diffusivity finite dimensional asymptotic behaviour of a semilinear wave equation |
| url | http://dx.doi.org/10.1155/S1110757X03212067 |
| work_keys_str_mv | AT robertwillie largediffusivityfinitedimensionalasymptoticbehaviourofasemilinearwaveequation |