Dynamics of wave equations with moving boundary

This paper is concerned with long-time dynamics of weakly damped semilinear wave equations defined on domains with moving boundary. Since the boundary is a function of the time variable the problem is intrinsically non-autonomous. Under the hypothesis that the lateral boundary is time-like, the solu...

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Detalles Bibliográficos
Autores: Ma, To Fu, Marín Rubio, Pedro, Surco Chuño, Christian Manuel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/84150
Acceso en línea:https://hdl.handle.net/11441/84150
https://doi.org/10.1016/j.jde.2016.11.030
Access Level:acceso abierto
Palabra clave:Wave equation
Non-cylindrical domain
Non-autonomous system
Pullback attractor
Critical exponent
Descripción
Sumario:This paper is concerned with long-time dynamics of weakly damped semilinear wave equations defined on domains with moving boundary. Since the boundary is a function of the time variable the problem is intrinsically non-autonomous. Under the hypothesis that the lateral boundary is time-like, the solution operator of the problem generates an evolution process U(t, τ ) : Xτ → Xt, where Xt are timedependent Sobolev spaces. Then, by assuming the domains are expanding, we establish the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the forcing terms. Our assumptions allow nonlinear perturbations with critical growth and unbounded time-dependent external forces.