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Toward the Fourier law for a weakly interacting anharmonic crystal

dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861
dc.contributor.authorLiverani, Carlangelo
dc.date.accessioned2010-07-22T15:34:09Z
dc.date.available2010-07-22T15:34:09Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4657
dc.language.isoenen
dc.subjecthypocoercivityen
dc.subjectWeak couplingen
dc.subjectscaling limitsen
dc.subjectGinzburg-Landau dynamicsen
dc.subjectheat equationen
dc.subjecthypoellipticityen
dc.subject.ddc519en
dc.titleToward the Fourier law for a weakly interacting anharmonic crystalen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenFor a system of weakly interacting anharmonic oscillators, perturbed by an energy preserving stochastic dynamics, we prove an autonomous (stochastic) evolution for the energies at large time scale (with respect to the coupling parameter). It turn out that this macroscopic evolution is given by the so called conservative (non-gradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics.en
dc.relation.isversionofjnlnameJournal of the American Mathematical Society
dc.relation.isversionofjnlvol25
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages555-583
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0894-0347-2011-00724-8
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00492016/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Mathematical Society
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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