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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 307 - 326, Volume 14, Issue 2, September 2010      doi:10.3934/dcdsb.2010.14.307

 
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María Anguiano - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
José Real - Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
José Valero - Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche, Spain (email)

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.

Received: September 2009;      Revised: February 2010;      Available Online: June 2010.