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| HAL: hal-00113806, version 2 |
| Detailed view |  Export this paper |
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| Asymptotic Analysis 59, 3-4 (2008) 125-138 |
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| Available versions: | v1 (2006-11-14) | v2 (2007-02-06) |
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| The Lévy-Fokker-Planck equation: Phi-entropies and convergence to equilibrium |
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| Ivan Gentil 1Cyril Imbert 2 |
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| (2008) |
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| In this paper, we study a Fokker-Planck equation of the form u_t = I [u ] + div (x u) where the operator I [u], which is usually the Laplacian, is replaced with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated equation. |
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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Fokker-Planck equation – Lévy operator – Phi-entropy inequalities – entropy production method – logarithmic Sobolev inequalities – fractional Laplacian |
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| hal-00113806, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00113806 | |
| oai:hal.archives-ouvertes.fr:hal-00113806 | |
| From: Cyril Imbert | |
| Submitted on: Tuesday, 6 February 2007 20:49:49 | |
| Updated on: Wednesday, 11 February 2009 06:37:54 | |
