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dc.contributor.authorImbert, Cyril
HAL ID: 9368
ORCID: 0000-0002-1290-8257
dc.contributor.authorMonneau, Régis
dc.contributor.authorRouy, Elisabeth
dc.date.accessioned2014-03-27T12:49:43Z
dc.date.available2014-03-27T12:49:43Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12970
dc.language.isoenen
dc.subjectperiodic homogenizationen
dc.subjectintegro-differential operatorsen
dc.subjectHamilton-Jacobi equationsen
dc.subjectdislocations dynamicsen
dc.subjectnon-periodic approximate correctorsen
dc.subject.ddc515en
dc.titleHomogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part II: application to dislocations dynamicsen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper is concerned with a result of homogenization of a non-local first order Hamilton-Jacobi equations describing the dislocations dynamics. Our model for the interaction between dislocations involve both an integro-differential operator and a (local) Hamiltonian depending periodicly on u=". The first two authors studied in a previous work homogenization problems involving such local Hamiltonians. Two main ideas of this previous work are used: on the one hand, we prove an ergodicity property of this equation by constructing approximate correctors which are necessarily non periodic in space in general; on the other hand, the proof of the convergence of the solution uses here a twisted perturbed test function for a higher dimensional problem. The limit equation is a nonlinear di usion equation involving a first order Lévy operator; the nonlinearity keeps memory of the short range interaction, while the Lévy operator keeps memory of long ones. The homogenized equation is a kind of effective plastic law for densities of dislocations moving in a single slip plane.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages30en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2007
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.submittednonen


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