dc.contributor.author Mischler, Stéphane dc.contributor.author Cañizo, José Alfredo dc.date.accessioned 2011-12-14T14:44:36Z dc.date.available 2011-12-14T14:44:36Z dc.date.issued 2011 dc.identifier.issn 0213-2230 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/7792 dc.language.iso en en dc.subject regularity dc.subject coagulation dc.subject self-similarity dc.subject uniqueness dc.subject asymptotic behavior dc.subject.ddc 515 en dc.title Regularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski's coagulation equation dc.type Article accepté pour publication ou publié dc.description.abstracten We consider Smoluchowski's equation with a homogeneous kernel of the form $a(x,y) = x^\alpha y ^\beta + x^\beta y^\alpha$ with $-1 < \alpha \leq \beta < 1$ and $\lambda := \alpha + \beta \in (-1,1)$. We first show that self-similar solutions of this equation are infinitely differentiable and prove sharp results on the behavior of self-similar profiles at $y = 0$ in the case $\alpha < 0$. We also give some partial uniqueness results for self-similar profiles: in the case $\alpha = 0$ we prove that two profiles with the same mass and moment of order $\lambda$ are necessarily equal, while in the case $\alpha < 0$ we prove that two profiles with the same moments of order $\alpha$ and $\beta$, and which are asymptotic at $y = 0$, are equal. Our methods include a new representation of the coagulation operator, and estimates of its regularity using derivatives of fractional order. dc.relation.isversionofjnlname Revista Matematica Iberoamericana dc.relation.isversionofjnlvol 27 dc.relation.isversionofjnlissue 3 dc.relation.isversionofjnldate 2011 dc.relation.isversionofjnlpages 803-839 dc.relation.isversionofdoi 10.4171/RMI/653 dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-00726385 dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Consejo Superior de Investigaciones Científicas dc.subject.ddclabel Analyse en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2017-10-25T08:42:50Z
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