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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
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 Narvik University College
Abstract : 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.
Keywords : homogenization effective diffusion singular perturbed operators logarithmic asymptotics random potential percolation theory
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https://hal.inria.fr/hal-00924088
Contributor : Fabien Campillo <>
Submitted on : Monday, January 6, 2014 - 12:11:17 PM
Last modification on : Wednesday, February 10, 2021 - 3:35:20 AM

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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⟩

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