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dc.contributor.authorJuengel, Ansgar
dc.contributor.authorGentil, Ivan
dc.contributor.authorDolbeault, Jean
dc.contributor.authorCarrillo, José
dc.date.accessioned2009-07-03T07:44:41Z
dc.date.available2009-07-03T07:44:41Z
dc.date.issued2006
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/712
dc.language.isoenen
dc.subjectlong-time behavioren
dc.subjecthigher-order nonlinear PDEsen
dc.subjectparabolic equationsen
dc.subjectSobolev estimatesen
dc.subjectPoincaré inequalityen
dc.subjectLogarithmic Sobolev inequalityen
dc.subjectthin film equation
dc.subjectfast diffusion equation
dc.subjectporous media equation
dc.subjectentropy-entropy production method
dc.subjectentropy production
dc.subjectentropy
dc.subject.ddc519en
dc.titleEntropy-Energy inequalities and improved convergence rates for nonlinear parabolic equationsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherJohannes Gutenberg Universitat;Allemagne
dc.contributor.editoruniversityotherUniversitat Autonoma de Barcelona;Espagne
dc.description.abstractenIn this paper, we prove new functional inequalities of Poincaré type on the one-dimensional torus $S^1$ and explore their implications for the long-time asymptotics of periodic solutions of nonlinear singular or degenerate parabolic equations of second and fourth order. We generically prove a global algebraic decay of an entropy functional, faster than exponential for short times, and an asymptotically exponential convergence of positive solutions towards their average. The asymptotically exponential regime is valid for a larger range of parameters for all relevant cases of application: porous medium/fast diffusion, thin film and logarithmic fourth order nonlinear diffusion equations. The techniques are inspired by direct entropy-entropy production methods and based on appropriate Poincaré type inequalities.en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series B
dc.relation.isversionofjnlvol6en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2006
dc.relation.isversionofjnlpages1027-1050en
dc.relation.isversionofdoihttp://dx.doi.org/10.3934/dcdsb.2006.6.1027
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00008520/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSouthwest Missouri State University Dept. of Mathematics
dc.subject.ddclabelProbabilités et Mathématiques appliquéesen


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