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| HAL: hal-00501842, version 2 |
| Detailed view |  Export this paper |
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| Available versions: | v2 (2012-03-16) | v3 (2012-06-19) |
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| Singularities of the Stationary Solutions to the Vlasov-Poisson System in a Polygon |
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| Fahd Karami 1, 2, 3Simon Labrunie 1, 2 |
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| For the CALVI ; CORIDA collaboration(s) |
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| (2012-03-16) |
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| We present an existence result for the stationary Vlasov--Poisson system in a bounded domain of~$\R^{N}$, with more general hypotheses than considered so far in the literature. In particular, we prove the equivalence of the kinetic approach (which consists in looking for the equilibrium distribution function) and the potential approach (where the unknown is the electrostatic potential at equilibrium). We study the dependence of the solution on parameters such as the total mass of the distribution, or those entering in the boundary conditions of the potential. Focusing on the case of a plane polygon, we study the singular behavior of the solution near the reentrant corners, and examine the dependence of the singularity coefficients on the parameters of the problem. Numerical experiments illustrate and confirm the analysis. |
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| 1: | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2: | CALVI (INRIA Nancy - Grand Est / IECN / LSIIT / IRMA) |
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CNRS : UMR7005 – INRIA – Université de Strasbourg – Université de Lorraine |
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| 3: | Ecole Supérieure de Technologie d'Essaouira |
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Université Cadi Ayyad (Marrakech, Maroc) |
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| 4: | CORIDA (INRIA Nancy - Grand Est / IECN / LMAM) |
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INRIA – CNRS : UMR7502 – Université de Lorraine |
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| Equations aux dérivées partielles |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Vlasov--Poisson system – Stationary solutions – Corner singularity – Nonlinear elliptic problem – Large solutions |
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| Attached file list to this document: | |||||
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| hal-00501842, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00501842 | |
| oai:hal.archives-ouvertes.fr:hal-00501842 | |
| From: Simon Labrunie | |
| Submitted on: Friday, 16 March 2012 13:30:02 | |
| Updated on: Wednesday, 21 March 2012 14:02:15 | |
