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

Authors
Millet, Annie Morien, Pierre-Luc
Citation
Millet, Annie et Morien, Pierre-luc, On a nonlinear stochastic wave equation in the plane: existence and uniqueness of the solution, Annals of applied probability , 11(3), 2001, pp. 922-951
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
11
Issue
3
Year of publication
2001
Pages
922 - 951
Database
ACNP
SICI code
Abstract
In 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.