Synchronization in coupled stochatic PDEs
Résumé : We deal with an abstract system of two coupled nonlinear stochastic (infinite dimensional) equations subjected to additive white noise type process. This kind of systems may describe various interaction phenomena in a continuum random medium. Under suitable conditions we prove the existence of an exponentially attracting random invariant manifold for the coupled system. This result means that under some conditions we observe (nonlinear) synchronization phenomena in the coupled system. As applications we consider stochastic systems consisting of (i) parabolic and hyperbolic equations, (ii) two hyperbolic equations, and (iii) Klein-Gordon and Schredinger equations.
Based on a joint paper with B. Schmalfuss.
Cet exposé se tiendra en salle C20-13, 20ème étage, Université Paris 1, Centre Pierre Mendes-France, 90 rue de Tolbiac, 75013 Paris (métro : Olympiades).