Rate of convergence to self-similarity for Smoluchowski's coagulation equation with constant coefficients

Cañizo, José Alfredo; Mischler, Stéphane; Mouhot, Clément

dc.contributor.author	Cañizo, José Alfredo
dc.contributor.author	Mischler, Stéphane
dc.contributor.author	Mouhot, Clément HAL ID: 1892
dc.date.accessioned	2010-01-20T12:46:23Z
dc.date.available	2010-01-20T12:46:23Z
dc.date.issued	2010
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/3049
dc.language.iso	en	en
dc.subject	Smoluchowski's equation	en
dc.subject	coagulation equation	en
dc.subject	constant coagulation kernel	en
dc.subject	self-similar variables	en
dc.subject	spectral gap	en
dc.subject	exponential relaxation rate	en
dc.subject	explicit	en
dc.subject.ddc	519	en
dc.title	Rate of convergence to self-similarity for Smoluchowski's coagulation equation with constant coefficients	en
dc.type	Article accepté pour publication ou publié
dc.contributor.editoruniversityother	Universitat Autónoma Barcelona;Espagne
dc.description.abstracten	We show that solutions to Smoluchowski's equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in a weighted Sobolev norm which implies the L² convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove these results through the study of the linearized coagulation equation in self-similar variables, for which we show a spectral gap in a scale of weighted Sobolev spaces. We also take advantage of the fact that the Laplace or Fourier transforms of this equation can be explicitly solved in this case.	en
dc.relation.isversionofjnlname	SIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol	41
dc.relation.isversionofjnlissue	6
dc.relation.isversionofjnldate	2010
dc.relation.isversionofjnlpages	2283-2314
dc.relation.isversionofdoi	http://dx.doi.org/10.1137/08074091X
dc.identifier.urlsite	http://hal.archives-ouvertes.fr/hal-00337661/en/	en
dc.description.sponsorshipprivate	oui	en
dc.relation.isversionofjnlpublisher	SIAM
dc.subject.ddclabel	Probabilités et mathématiques appliquées	en

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Rate of convergence to self-similarity for Smoluchowski's coagulation equation with constant coefficients

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