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Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains

 

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Opened Access Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains
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Author: Anguiano Moreno, María
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2010
Published in: Boletín de la Sociedad Española de Matemática Aplicada, 51, 9-16.
Document type: Article
Abstract: The existence of a pullback attractor in L2(Ω) for the following nonautonomous reaction-di usion equation ∂u ∂t − △u = f(u) + h(t), in Ω × (τ, +∞), u = 0, on ∂Ω × (τ, +∞), u(x, τ ) = uτ (x), x ∈ Ω, is proved in this paper, when the domain Ω is not necessarily bounded but satisfying the Poincaré inequality, and h ∈ L2 loc(R; H−1(Ω)). The main concept used in the proof is the asymptotic compactness of the process generated by the problem.
Cite: Anguiano Moreno, M. (2010). Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains. Boletín de la Sociedad Española de Matemática Aplicada, 51, 9-16.
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URI: http://hdl.handle.net/11441/43841

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