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| HAL: hal-00409935, version 1 |
| arXiv: 0908.2226 |
| DOI: 10.1016/j.aml.2010.08.020 |
| Detailed view |  Export this paper |
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| Applied Mathematics Letters 24, 1 (2011) 76 - 81 |
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| Improved intermediate asymptotics for the heat equation |
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| Jean-Philippe Bartier 1Adrien Blanchet 2 |
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| (2011) |
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| This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the stationary solution, we get improved convergence rates using entropy / entropy-production methods. We establish the equivalence of the exponential decay of the entropies with new, improved functional inequalities in restricted classes of functions. This letter is the counterpart in a linear framework of a recent work on fast diffusion equations, see [Bonforte-Dolbeault-Grillo-Vazquez]. Results extend to the case of a Fokker-Planck equation with a general confining potential. |
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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: | Groupe de recherche en économie mathématique et quantitative (GREMAQ) |
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CNRS : UMR5604 – Université des Sciences Sociales - Toulouse I – École des Hautes Études en Sciences Sociales [EHESS] – Institut national de la recherche agronomique (INRA) : UMR |
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| 3: | Departamento de Matemáticas |
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Universidad del País Vasco |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Heat equation – Fokker-Planck equation – Ornstein-Uhlenbeck equation – intermediate asymptotics – self-similar variables – stationary solutions – large time behavior – rate of convergence – entropy – Poincar inequality – logarithmic Sobolev inequality – interpolation inequalities |
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| Attached file list to this document: | ||||||||||
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| hal-00409935, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00409935 | |
| oai:hal.archives-ouvertes.fr:hal-00409935 | |
| From: Jean Dolbeault | |
| Submitted on: Friday, 14 August 2009 13:42:04 | |
| Updated on: Wednesday, 27 October 2010 23:12:06 | |
