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| HAL : hal-00371068, version 1 |
| arXiv : 0903.4679 |
| Fiche détaillée |  Récupérer au format |
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| Large time behavior of solutions of viscous Hamilton-Jacobi Equations with superquadratic Hamiltonian |
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| Thierry Wilfried Tabet Tchamba 1 |
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| (26/03/2009) |
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| We study the long-time behavior of the unique viscosity solution $u$ of the viscous Hamilton-Jacobi Equation $u_t-\Delta u + |Du|^m = f\hbox{ in }\Omega\times (0,+\infty)$ with inhomogeneous Dirichlet boundary conditions, where $\Omega$ is a bounded domain of $\mathbb{R}^N$. We mainly focus on the superquadratic case ($m>2$) and consider the Dirichlet conditions in the generalized viscosity sense. Under rather natural assumptions on $f,$ the initial and boundary data, we connect the problem studied to its associated stationary generalized Dirichlet problem on one hand and to a stationary problem with a state constraint boundary condition on the other hand. |
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| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| hal-00371068, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00371068 | |
| oai:hal.archives-ouvertes.fr:hal-00371068 | |
| Contributeur : Thierry Wilfried Tabet Tchamba | |
| Soumis le : Jeudi 26 Mars 2009, 14:16:32 | |
| Dernière modification le : Jeudi 26 Mars 2009, 20:43:29 | |
