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dc.contributor.authorSaint-Pierre, Patrick
dc.contributor.authorBayen, Alexandre M.
dc.contributor.authorAubin, Jean-Pierre
dc.date.accessioned2010-09-17T09:35:52Z
dc.date.available2010-09-17T09:35:52Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4810
dc.language.isoenen
dc.subjectHamilton Jacobi equationen
dc.subjecttraffic modelingen
dc.subjectoptimal controlen
dc.subjectviability theoryen
dc.subject.ddc519en
dc.titleDirichlet Problems for some Hamilton-Jacobi Equations With Inequality Constraintsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Civil and Environmental Engineering, University of California at Berkeley;États-Unis
dc.description.abstractenWe use viability techniques for solving Dirichlet problems with inequality constraints (obstacles) for a class of Hamilton-Jacobi equations. The hypograph of the "solution" is defined as the "capture basin" under an auxiliary control system of a target associated with the initial and boundary conditions, viable in an environment associated with the inequality constraint. From the tangential condition characterizing capture basins, we prove that this solution is the unique "upper semicontinuous" solution to the Hamilton-Jacobi-Bellman partial differential equation in the Barron-Jensen/Frankowska sense. We show how this framework allows us to translate properties of capture basins into corresponding properties of the solutions to this problem. For instance, this approach provides a representation formula of the solution which boils down to the Lax-Hopf formula in the absence of constraintsen
dc.relation.isversionofjnlnameSIAM journal on control and optimization
dc.relation.isversionofjnlvol47en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages2348-2380en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/060659569en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSociety for Industrial and Applied Mathematicsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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