International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 43, Pages 2735-2746
doi:10.1155/S0161171203211121

On a stochastic Burgers equation with Dirichlet boundary conditions

Abstract

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.