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A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations

Abstract : We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary condition and Dirichlet boundary condition. We establish general convergence results for viscosity solutions to asymptotic solutions as time goes to infinity via an approach based on PDE techniques. These results are obtained not only under general conditions on the Hamiltonians but also under weak conditions on the domain and the oblique direction of reflection in the Neumann case.
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https://hal.archives-ouvertes.fr/hal-00542225
Contributor : Guy Barles <>
Submitted on : Friday, December 10, 2010 - 9:59:06 AM
Last modification on : Friday, October 25, 2019 - 12:18:28 PM
Document(s) archivé(s) le : Friday, March 11, 2011 - 3:07:50 AM

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  • HAL Id : hal-00542225, version 2
  • ARXIV : 1012.0688

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Guy Barles, Hiroyoshi Mitake. A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations. Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (1), pp.136-168. ⟨hal-00542225v2⟩

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