Differential and Integral Equations
- Differential Integral Equations
- Volume 21, Number 11-12 (2008), 1055-1082.
Stochastic perturbation of nonlinear degenerate parabolic problems
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.
Differential Integral Equations, Volume 21, Number 11-12 (2008), 1055-1082.
First available in Project Euclid: 14 December 2012
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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