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| HAL : hal-00627812, version 2 |
| arXiv : 1109.6765 |
| DOI : 10.1142/S1793744211000461 |
| Fiche détaillée |  Récupérer au format |
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| Confluentes Mathematici (CM) 03, 04 (2012) 617-635 |
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| Versions disponibles : | v1 (30-09-2011) | v2 (11-10-2011) |
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| On the gradient flow of a one-homogeneous functional |
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| Ariela Briani 1Antonin Chambolle 2 |
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| (03/2012) |
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| We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of the Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a consequence we get existence and uniqueness of a weak solution to the Hele-Shaw flow. We also obtain an explicit representation for the Total Variation flow in one dimension and easily deduce basic qualitative properties, concerning in particular the ''staircasing effect''. |
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| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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Université François Rabelais - Tours – CNRS : UMR7350 |
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| 2 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 3 : | Dipartimento di Matematica Pura ed Applicata |
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Università degli studi di Padova |
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| 4 : | Department of Computer Science / Dipartimento di Informatica [Verona] |
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University of Verona – Università degli studi di Verona |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00627812, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00627812 | |
| oai:hal.archives-ouvertes.fr:hal-00627812 | |
| Contributeur : Ariela Briani | |
| Soumis le : Mardi 11 Octobre 2011, 14:37:53 | |
| Dernière modification le : Vendredi 1 Mars 2013, 17:38:08 | |
