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| HAL: hal-00668298, version 1 |
| arXiv: 1202.2031 |
| Detailed view |  Export this paper |
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| Degenerate parabolic SPDEs |
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| Martina Hofmanova 1 |
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| (2012-02-09) |
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| We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic solution which is well suited for degenerate parabolic problems and supplies a good technical framework to prove the comparison principle. The proof of existence is based on the vanishing viscosity method: the solution is obtained by a compactness argument as the limit of solutions of nondegenerate approximations. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Processus stochastiques, Analyse numérique |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Probability |
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| degenerate parabolic stochastic partial differential equation – kinetic solution |
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| hal-00668298, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00668298 | |
| oai:hal.archives-ouvertes.fr:hal-00668298 | |
| From: Maryse Collin | |
| Submitted on: Thursday, 9 February 2012 15:23:06 | |
| Updated on: Thursday, 9 February 2012 17:14:55 | |
