Stabilization of stationary solutions of evolution equations bynoise

Tomás Caraballo; P.E. Kloeden; B. Schmalfuss

doi:10.3934/dcdsb.2006.6.1199

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2006, Volume 6, Issue 6: 1199-1212. Doi: 10.3934/dcdsb.2006.6.1199

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Stabilization of stationary solutions of evolution equations by noise

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla
2.
FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
3.
Institut für Mathematik Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn

Received: December 31, 2005

Revised: March 31, 2006

Published: October 2006

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Abstract

We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic semilinear evolution equations. Our main result shows, in particular, that noise can have a stabilization effect on deterministic equations. Moreover, we do not require any commutative condition on the noise terms.

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Mathematics Subject Classification: Primary: 60H15, 35K40.

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