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| Fiche détaillée | Preprint, Working Paper, Document sans référence, etc. |
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| Versions disponibles : | v1 (01-02-2011) | v2 (24-02-2011) |
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| Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs |
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| Boris Andreianov1 |
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| We discuss several techniques for proving compactness of sequences of approximate solutions to discretized evolution PDEs. While the well-known Aubin-Simon kind functional-analytic techniques were recently generalized to the discrete setting by Gallouët and Latché [15], here we discuss direct techniques for estimating the time translates of approximate solutions in the space $L^1$. One important result is the Kruzhkov time compactness lemma. Further, we describe a specific technique that relies upon the order-preservation property. Motivation comes from studying convergence of finite volume discretizations for various classes of nonlinear degenerate parabolic equations. These and other applications are briefly described. |
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| 1 : | LM-Besançon - Laboratoire de Mathématiques |
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| Compactness – Time translates – Kruzhkov lemma – Order-preservation – Finite volumes |
| hal-00561344, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00561344 | |
| oai:hal.archives-ouvertes.fr:hal-00561344 | |
| Contributeur : Boris Andreianov | |
| Soumis le : Jeudi 24 Février 2011, 14:03:49 | |
| Dernière modification le : Jeudi 24 Février 2011, 15:48:30 | |
