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dc.contributor.authorMischler, Stéphane
dc.contributor.authorCañizo, José Alfredo
dc.date.accessioned2011-12-14T14:44:36Z
dc.date.available2011-12-14T14:44:36Z
dc.date.issued2011
dc.identifier.issn0213-2230
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7792
dc.language.isoenen
dc.subjectregularity
dc.subjectcoagulation
dc.subjectself-similarity
dc.subjectuniqueness
dc.subjectasymptotic behavior
dc.subject.ddc515en
dc.titleRegularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski's coagulation equation
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe 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.isversionofjnlnameRevista Matematica Iberoamericana
dc.relation.isversionofjnlvol27
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages803-839
dc.relation.isversionofdoi10.4171/RMI/653
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00726385
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherConsejo Superior de Investigaciones Científicas
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-10-25T08:42:50Z


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