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dc.contributor.authorCardaliaguet, Pierre*
dc.contributor.authorSouganidis, Panagiotis E.*
dc.date.accessioned2011-10-19T14:24:45Z
dc.date.available2011-10-19T14:24:45Z
dc.date.issued2013
dc.identifier.issn0010-3640
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7256
dc.language.isoenen
dc.subjectviscosity solutions
dc.subjectHamilton-Jacobi equations
dc.subjecthomogenization
dc.subjectergodic media
dc.subject.ddc515en
dc.titleHomogenization and enhancement of the G-equation in random environments
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of mathematics http://www.math.uchicago.edu/ Université de Chicago;États-Unis
dc.description.abstractenWe study the homogenization of a $G$-equation which is advected by a divergence free stationary vector field in a general ergodic random environment. We prove that the averaged equation is an anisotropic deterministic G-equation and we give necessary and sufficient conditions in order to have enhancement. Since the problem is not assumed to be coercive it is not possible to have uniform bounds for the solutions. In addition, as we show, the associated minimal (first passage) time function does not satisfy, in general, the uniform integrability condition which is necessary to apply the sub-additive ergodic theorem. We overcome these obstacles by (i) establishing a new reachability (controllability) estimate for the minimal function and (ii) constructing, for each direction and almost surely, a random sequence which has both a long time averaged limit (due to the sub-additive ergodic theorem) and stays (in the same sense) asymptotically close to the minimal time.
dc.relation.isversionofjnlnameCommunications on Pure and Applied Mathematics
dc.relation.isversionofjnlvol66
dc.relation.isversionofjnlissue10
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages1582–1628
dc.relation.isversionofdoihttp://dx.doi.org/10.1002/cpa.21449
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherWiley
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2019-02-22T10:29:12Z
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