Affiliations: LPMA, Université Diderot Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France. E-mail: delarue@math.jussieu.fr | CEREMADE, Université Paris Dauphine, Place du marcéchal De Lattre de Tassigny, 75775 Paris Cedex 16, France. E-mail: rhodes@ceremade.dauphine.fr
Note: [] Corresponding author: François Delarue, LPMA, Université Diderot Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France. Tel.: +33 01 44277623; E-mail: delarue@math.jussieu.fr.
Abstract: We investigate stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is ergodic, we can prove the homogenization property for the quasilinear PDEs, by means of the first-order approximation method. The (nonlinear) limit operator need not be nondegenerate. Concrete examples are provided.
