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| HAL : hal-00444392, version 1 |
| arXiv : 1001.0910 |
| Fiche détaillée |  Récupérer au format |
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| Fractal porous media equation |
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| Piotr Biler 1Cyril Imbert 2 |
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| Polonium 20078TL Collaboration(s) |
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| (06/01/2010) |
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| We study a generalization of the porous medium equation involving nonlocal terms. In particular, the $L^p$ decay of solutions of the Cauchy problem is proved. Explicit self-similar solutions with compact support generalizing the KZB (or Barenblatt) solutions are constructed in the case corresponding to transport equation with a nonlocal velocity. |
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| 1 : | Instytut Matematyczny |
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Uniwersytet Wroclawski |
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| 2 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris Dauphine - Paris IX |
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| 3 : | Instytut Matematyczny |
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Uniwersytet Wroclawski |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Self-similar solutions – $L^p$-estimates – porous medium equation – Riesz potential – fractional Laplacian |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00444392, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00444392/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00444392_v1 | |
| Contributeur : Cyril Imbert | |
| Soumis le : Mercredi 6 Janvier 2010, 15:08:31 | |
| Dernière modification le : Mercredi 6 Janvier 2010, 15:44:07 | |
