On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

Abstract : In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the ''weak KAM approach'' which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets.
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Article dans une revue
Archive for Rational Mechanics and Analysis, Springer Verlag, 2012, 204 (2), pp.515-558
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https://hal.archives-ouvertes.fr/hal-00623000
Contributeur : Guy Barles <>
Soumis le : jeudi 12 janvier 2012 - 07:54:22
Dernière modification le : vendredi 15 mars 2019 - 17:24:11
Document(s) archivé(s) le : vendredi 13 avril 2012 - 02:22:49

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  • HAL Id : hal-00623000, version 2
  • ARXIV : 1109.2762

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Guy Barles, Hiroyoshi Mitake, Hitoshi Ishii. On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions. Archive for Rational Mechanics and Analysis, Springer Verlag, 2012, 204 (2), pp.515-558. 〈hal-00623000v2〉

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