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Asymptotic Analysis (2009) 61--90

Stochastic Homogenization of Quasilinear PDEs with a Spatial Degeneracy

Francois Delarue 1, Rémi Rhodes 2

(2009-01-21)

We investigate stochastic homogenization for some degenerate quasilinear pa rabolic 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 needn't be nondegenerate. Concrete examples are provided.

1:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
2:	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Subject

:

Mathematics/Probability

Keyword(s): Stochastic homogenization – parabolic PDE – nonlinear PDE – degenerate PDE – first order approximation – ergodic operator.

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From: Francois Delarue <>

Submitted on: Wednesday, 11 April 2007 20:36:51

Updated on: Wednesday, 2 February 2011 21:49:29