November  2006, 6(6): 1199-1212. doi: 10.3934/dcdsb.2006.6.1199

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, Spain

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, Germany

Received  January 2006 Revised  April 2006 Published  August 2006

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.
Citation: Tomás Caraballo, P.E. Kloeden, B. Schmalfuss. Stabilization of stationary solutions of evolution equations by noise. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1199-1212. doi: 10.3934/dcdsb.2006.6.1199
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