Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions

Pages: 439 - 455, Volume 14, Issue 2, September 2010

doi:10.3934/dcdsb.2010.14.439       Abstract        Full Text (225.4K)       Related Articles

Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
María J. Garrido–Atienza - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Björn Schmalfuss - Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany (email)
José Valero - Dpto. Estadística y Matemática Aplicada, Universidad Miguel Hernández, Avda. de la Universidad, s/n, 03202 Elche, Spain (email)

Abstract: In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations with infinite delays when the uniqueness of solutions for these equations is not required. Our results are obtained by means of the theory of set-valued random dynamical systems and their conjugation properties.

Keywords:  Multivalued non-autonomous and random dynamical systems, pullback and random attractors, functional stochastic equations, conjugacy method.
Mathematics Subject Classification:  60H15, 35K40.

Received: February 2009;      Revised: July 2009;      Published: June 2010.