On a non linear stochastic wave equation in the plane: existence and uniqueness of the solution

Annie Millet (1, 2) , Pierre-Luc Morien (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 MODAL'X - Modélisation aléatoire de Paris X

n this paper, we investigate the existence and uniqueness of the solution for a class of stochastic wave equations in two space-dimensions containing a non-linearity of polynomial type. The method used in the proofs combines functional analysis arguments with probabilistic tools, and furher estimates for the Green function associated with the classical wave equation.

Mots clés: stochastic partial differential equations; wave equation; Gaussian noise; apriori estimates

Domaines: Probabilités [math.PR]

Annie Millet, Pierre-Luc Morien. On a non linear stochastic wave equation in the plane: existence and uniqueness of the solution. The Annals of Applied Probability, 2001, 11 (3), pp.922-951. ⟨10.1214/aoap/1015345353⟩. ⟨hal-00258030⟩