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Dynamics of wave equations with moving boundary


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Author: Ma, To Fu
Marín Rubio, Pedro
Surco Chuño, Christian Manuel
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2017-03-05
Published in: Journal of Differential Equations, 262 (5), 3317-3342.
Document type: Article
Abstract: 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.
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DOI: 10.1016/j.jde.2016.11.030

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