Differential and Integral Equations

Stochastic perturbation of nonlinear degenerate parabolic problems

G. Vallet

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Abstract

In this paper, we are interested in nonlinear stochastic partial differential equations. Stochastic perturbations of a class of degenerate parabolic problems with homogeneous Dirichlet boundary conditions are considered. A time-discretization is used to prove the existence of a solution. The pivot-space method leads to the uniqueness. Then, applications to the porous media and the Buckley-Leverett equations are proposed.

Article information

Source
Differential Integral Equations, Volume 21, Number 11-12 (2008), 1055-1082.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355502294

Mathematical Reviews number (MathSciNet)
MR2482497

Zentralblatt MATH identifier
1224.35218

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K65: Degenerate parabolic equations 60H15: Stochastic partial differential equations [See also 35R60]

Citation

Vallet, G. Stochastic perturbation of nonlinear degenerate parabolic problems. Differential Integral Equations 21 (2008), no. 11-12, 1055--1082. https://projecteuclid.org/euclid.die/1355502294


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