A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the non-linear term f. The function β"(t) depends on a parameter ε, β&q...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23632 |
| Acceso en línea: | http://hdl.handle.net/11441/23632 https://doi.org/10.1016/j.na.2010.11.032 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-autonomous damped wave equation Existence and structure of the pullback attractor Lower and upper semicontinuity |
| Sumario: | In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the non-linear term f. The function β"(t) depends on a parameter ε, β"(t) "!0 −→ 0. We will prove, under suitable assumptions, local and global well posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A"(t) : t ∈ R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at ǫ = 0. |
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