Pullback attractors for reaction-diffusion equations in some unbounded domainswith an $H^{-1}$-valued non-autonomous forcing term and withoutuniqueness of solutions

María Anguiano; Tomás Caraballo; José Real; José Valero

doi:10.3934/dcdsb.2010.14.307

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2010, Volume 14, Issue 2: 307-326. Doi: 10.3934/dcdsb.2010.14.307

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Pullback attractors for reaction-diffusion equations in some unbounded domains with an $H^{-1}$-valued non-autonomous forcing term and without uniqueness of solutions

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080-Sevilla
2.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
3.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
4.
Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche

Received: September 2009

Revised: February 2010

Published: September 2010

Abstract / Introduction Related Papers Cited by

Abstract

The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous forcing term taking values in the space $H^{-1}$, and with a continuous nonlinearity which does not ensure uniqueness of solutions, is proved in this paper. The theory of set-valued non-autonomous dynamical systems is applied to the problem.

Keywords:

Pullback attractor,
asymptotic compactness,
multivalued evolution process,
non-autonomous reaction-diffusion equation.

Mathematics Subject Classification: 35Q35, 35Q30, 35K90, 37L30.

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Pullback attractors for reaction-diffusion equations in some unbounded domains with an $H^{-1}$-valued non-autonomous forcing term and without uniqueness of solutions

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