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dc.contributor.authorNolen, James*
hal.structure.identifier
dc.contributor.authorCardaliaguet, Pierre*
hal.structure.identifier
dc.contributor.authorSouganidis, Panagiotis E.*
dc.date.accessioned2011-09-06T14:27:24Z
dc.date.available2011-09-06T14:27:24Z
dc.date.issued2011
dc.identifier.issn0003-9527
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6918
dc.language.isoenen
dc.subjectG-equation
dc.subjectHamilton-Jacobi equation
dc.subject.ddc515en
dc.titleHomogenization and Enhancement for the G—Equation
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the so-called G-equation, a level set Hamilton–Jacobi equation used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover, we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally, we also consider advection depending on position at the integral scale.
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol199
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages527-561
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00205-010-0332-8
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2019-02-22T10:29:52Z
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