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arXiv · 1202.2031

Degenerate parabolic SPDEs

Martina Hofmanova
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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.

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Martina Hofmanova. 2012-02-09. Degenerate parabolic SPDEs. https://arxiv.org/abs/1202.2031

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