Stochastic parabolic systems with memory terms
Résumé : The existence and uniqueness of solutions for stochastic reaction-diffusion equation with infinite delay is proved. Sufficient conditions ensuring stability of the zero solution are provided and a possibility of stabilization by noise of the deterministic counterpart of the model is studied. In the case of additive noise we prove that the equation generates a random dynamical system in an appropriate phase space which possesses the random pullback attractor.
Some of the results were established in collaboration with T. Caraballo, P. Marin-Rubio and J. Real
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).