Effective diffusion in vanishing viscosity

Fabien Campillo (1, 2) , Andrey L. Piatnitski (3)

1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 Narvik University College

We study the asymptotic behavior of effective diffusion for singular perturbed elliptic operators with potential first order terms. Assuming that the potential is a random perturbation of a fixed periodic function and that this perturbation does not affect essentially the structure of the potential, we prove the exponential decay of the effective diffusion. Moreover, we establish its logarithmic asymptotics in terms of proper percolation level for the random potential.

Mots clés: homogenization; effective diffusion; singular perturbed operators; logarithmic asymptotics; random potential; percolation theory

Domaines: Probabilités [math.PR]

Fabien Campillo, Andrey L. Piatnitski. Effective diffusion in vanishing viscosity. D. Cioranescu and J.-L. Lions. Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XIV (Paris, 1997/1998), 31, North-Holland, pp.133--145, 2002. ⟨hal-00924088⟩