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Pré-Publication, Document De Travail Année : 2011

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

Résumé

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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Dates et versions

hal-00623000 , version 1 (13-09-2011)
hal-00623000 , version 2 (12-01-2012)

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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. 2011. ⟨hal-00623000v1⟩
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