Degenerate parabolic stochastic partial differential equations

Martina Hofmanová

Stochastic Processes and their Applications, 2013, vol. 123, issue 12, 4294-4336

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.

Keywords: Degenerate parabolic stochastic partial differential equation; Kinetic solution (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.06.015

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