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On a stochastic Burgers equation with Dirichlet boundary conditions. (English) Zbl 1030.60048
The author proves the existence of a weak solution for the one-dimensional Burgers equation perturbed by a white noise term, with Dirichlet boundary conditions and a continuous (not necessarily Lipschitz) coefficient. The sequence of polygonal approximations is proved to be tight, and the martingale problem for the weak limit has a solution.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H40 White noise theory
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