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).