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.
"Stochastic perturbation of nonlinear degenerate parabolic problems." Differential Integral Equations 21 (11-12) 1055 - 1082, 2008.