Degenerate parabolic SPDEs
Analysis of PDEs
2012-02-10 v1 Probability
Abstract
We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic solution which is well suited for degenerate parabolic problems and supplies a good technical framework to prove the comparison principle. The proof of existence is based on the vanishing viscosity method: the solution is obtained by a compactness argument as the limit of solutions of nondegenerate approximations.
Cite
@article{arxiv.1202.2031,
title = {Degenerate parabolic SPDEs},
author = {Martina Hofmanova},
journal= {arXiv preprint arXiv:1202.2031},
year = {2012}
}