Degenerate parabolic SPDEs

2012/02/09 by Martina Hofmanová, Hofmanova, Martina
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1202.2031

openalex publication_date 2012/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Well-posedness and regularity for quasilinear degenerate\n parabolic-hyperbolic SPDE
• On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with\n L 'evy noise
• A fractional degenerate parabolic-hyperbolic Cauchy problem with noise
• A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations
• A Boundary Value Problem for a Class of Anisotropic Stochastic Degenerate Parabolic-Hyperbolic Equations