Homogenization of transport equations: A simple PDE approach to the Kubo formula |
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| Authors: | Thierry Goudon Frédéric Poupaud |
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| Institution: | a Team SIMPAF-INRIA Futurs & Laboratoire Paul Painlevé, UMR 8524, CNRS-Université des Sciences et Technologies de Lille, Cité Scientifique, F-59655 Villeneuve d'Ascq Cedex, France
b Laboratoire J. A. Dieudonné, UMR 6621, CNRS-Université Nice-Sophia Antipolis, Parc Valrose, F-06108 Nice Cedex 2, France |
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| Abstract: | We are interested in the behavior with respect to the small parameter ?>0 of solutions ρ? of the conservative transport(-diffusion) equation t∂ρ?+∇x(ρ?u?)=ηΔxρ?, with η?0, driven by a large random velocity field: |u?|=O(1/?). Assuming that the velocity does not have long-time memory we justify the convergence of the expectation Eρ? to the solution of a diffusion equation. This question has been widely investigated; here we present a simple proof which only relies on PDE tools. |
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| Keywords: | 60H30 35Q35 |
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