Energy decay for solutions to semilinear systems of elastic waves in exterior domains
We consider the dynamical system of elasticity in the exterior of a bounded open domain in 3-D with smooth boundary. We prove that under the effect of "weak" dissipation, the total energy decays at a uniform rate as $t o +infty$, provided the initial data is "small" at in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2006-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/65/abstr.html |
| _version_ | 1818473916476162048 |
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| author | Marcio V. Ferreira Gustavo P. Menzala |
| author_facet | Marcio V. Ferreira Gustavo P. Menzala |
| author_sort | Marcio V. Ferreira |
| collection | DOAJ |
| description | We consider the dynamical system of elasticity in the exterior of a bounded open domain in 3-D with smooth boundary. We prove that under the effect of "weak" dissipation, the total energy decays at a uniform rate as $t o +infty$, provided the initial data is "small" at infinity. No assumptions on the geometry of the obstacle are required. The results are then applied to a semilinear problem proving global existence and decay for small initial data. |
| first_indexed | 2024-04-14T04:30:20Z |
| format | Article |
| id | doaj.art-1960b9783b5b4fe39b16b93c9bfb2de2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T04:30:20Z |
| publishDate | 2006-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1960b9783b5b4fe39b16b93c9bfb2de22022-12-22T02:12:06ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-05-01200665113Energy decay for solutions to semilinear systems of elastic waves in exterior domainsMarcio V. FerreiraGustavo P. MenzalaWe consider the dynamical system of elasticity in the exterior of a bounded open domain in 3-D with smooth boundary. We prove that under the effect of "weak" dissipation, the total energy decays at a uniform rate as $t o +infty$, provided the initial data is "small" at infinity. No assumptions on the geometry of the obstacle are required. The results are then applied to a semilinear problem proving global existence and decay for small initial data.http://ejde.math.txstate.edu/Volumes/2006/65/abstr.htmlUniform stabilizationexterior domainsystem of elastic wavessemilinear problem. |
| spellingShingle | Marcio V. Ferreira Gustavo P. Menzala Energy decay for solutions to semilinear systems of elastic waves in exterior domains Electronic Journal of Differential Equations Uniform stabilization exterior domain system of elastic waves semilinear problem. |
| title | Energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| title_full | Energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| title_fullStr | Energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| title_full_unstemmed | Energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| title_short | Energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| title_sort | energy decay for solutions to semilinear systems of elastic waves in exterior domains |
| topic | Uniform stabilization exterior domain system of elastic waves semilinear problem. |
| url | http://ejde.math.txstate.edu/Volumes/2006/65/abstr.html |
| work_keys_str_mv | AT marciovferreira energydecayforsolutionstosemilinearsystemsofelasticwavesinexteriordomains AT gustavopmenzala energydecayforsolutionstosemilinearsystemsofelasticwavesinexteriordomains |