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| HAL : hal-00281709, version 1 |
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| On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations |
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Gloria Aguilar 1Laurent Levi 2 |
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| (23/05/2008) |
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| This paper deals with the coupling of a quasilinear parabolic problem with a first order hyperbolic one in a multidimensional bounded domain $\Omega $. In a region $\Omega _{p}$ a diffusion-advection-reaction type equation is set while in the complementary $\Omega _{h}\equiv \Omega \backslash \Omega _{p}$, only advection-reaction terms are taken into account. Suitable transmission conditions along the interface $\partial \Omega _{p}\cap \partial \Omega _{h}$ are required. We select a weak solution characterized by an entropy inequality on the whole domain. This solution is given by a vanishing viscosity method. |
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| 1 : | Université de Saragosse |
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Université de Saragosse |
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| 2 : | Laboratoire de Mathématiques et de leurs Applications de Pau (LMA-PAU) |
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CNRS : UMR5142 – Université de Pau et des Pays de l'Adour [UPPA] |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Coupling problem – degenerate parabolic-hyperbolic equation – entropy solution |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00281709, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00281709 | |
| oai:hal.archives-ouvertes.fr:hal-00281709 | |
| Contributeur : Laurent Lévi | |
| Soumis le : Lundi 26 Mai 2008, 11:09:24 | |
| Dernière modification le : Lundi 26 Mai 2008, 13:40:21 | |
