Attractors for a class of semi-linear degenerate parabolic equations
We consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence of solutions and characterize their longtime behavior. In particular, we show...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/523 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/523 |
| Access Level: | acceso abierto |
| Palabra clave: | global attractors gradient semigroups longtime behavior of solutions Semilinear degenerate parabolic equations |
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Attractors for a class of semi-linear degenerate parabolic equationsKogoj, A.E.Sonner, S.global attractorsgradient semigroupslongtime behavior of solutionsSemilinear degenerate parabolic equationsWe consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence of solutions and characterize their longtime behavior. In particular, we show the existence and finite fractal dimension of the global attractor of the generated semigroup and the convergence of solutions to an equilibrium solution when time tends to infinity.201720172013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/523reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84892890818&doi=10.1007%2fs00028-013-0196-0&partnerID=40&md5=60d430bb0642b7b371ad5acacddb5b9eReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/5232026-06-19T12:47:47Z |
| dc.title.none.fl_str_mv |
Attractors for a class of semi-linear degenerate parabolic equations |
| title |
Attractors for a class of semi-linear degenerate parabolic equations |
| spellingShingle |
Attractors for a class of semi-linear degenerate parabolic equations Kogoj, A.E. global attractors gradient semigroups longtime behavior of solutions Semilinear degenerate parabolic equations |
| title_short |
Attractors for a class of semi-linear degenerate parabolic equations |
| title_full |
Attractors for a class of semi-linear degenerate parabolic equations |
| title_fullStr |
Attractors for a class of semi-linear degenerate parabolic equations |
| title_full_unstemmed |
Attractors for a class of semi-linear degenerate parabolic equations |
| title_sort |
Attractors for a class of semi-linear degenerate parabolic equations |
| dc.creator.none.fl_str_mv |
Kogoj, A.E. Sonner, S. |
| author |
Kogoj, A.E. |
| author_facet |
Kogoj, A.E. Sonner, S. |
| author_role |
author |
| author2 |
Sonner, S. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
global attractors gradient semigroups longtime behavior of solutions Semilinear degenerate parabolic equations |
| topic |
global attractors gradient semigroups longtime behavior of solutions Semilinear degenerate parabolic equations |
| description |
We consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence of solutions and characterize their longtime behavior. In particular, we show the existence and finite fractal dimension of the global attractor of the generated semigroup and the convergence of solutions to an equilibrium solution when time tends to infinity. |
| publishDate |
2013 |
| dc.date.none.fl_str_mv |
2013 2017 2017 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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http://hdl.handle.net/20.500.11824/523 |
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http://hdl.handle.net/20.500.11824/523 |
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Inglés |
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Inglés |
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84892890818&doi=10.1007%2fs00028-013-0196-0&partnerID=40&md5=60d430bb0642b7b371ad5acacddb5b9e |
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Reconocimiento-NoComercial-CompartirIgual 3.0 España http://creativecommons.org/licenses/by-nc-sa/3.0/es/ info:eu-repo/semantics/openAccess |
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Reconocimiento-NoComercial-CompartirIgual 3.0 España http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
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openAccess |
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application/pdf |
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reponame:BIRD. BCAM's Institutional Repository Data instname:Basque Center for Applied Mathematics (BCAM) |
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Basque Center for Applied Mathematics (BCAM) |
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BIRD. BCAM's Institutional Repository Data |
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BIRD. BCAM's Institutional Repository Data |
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