International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 43, Pages 2735-2746
On a stochastic Burgers equation with Dirichlet boundary conditions
Centro de Investigacion en Matematicas (CIMAT), Guanajuato 36000, CP, Mexico
Received 5 November 2002
Copyright © 2003 Ekaterina T. Kolkovska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.