Uniqueness and regularity of scaling profiles for Smoluchowskis coagulation equationReportar como inadecuado




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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision 2 Departament de Matemàtiques Barcelona

Abstract : We consider Smoluchowski-s equation with a homogeneous kernel of the form ax, y = xαyβ + yβxα with −1 < α ≤ β ≤ 1 and λ := α+β ∈ 0, 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 α < 0. We also give some partial uniqueness results for self-similar profiles: in the case α = 0 we prove that two profiles with the same mass and moment of order λ are necessarily equal, while in the case α < 0 we prove that two profiles with the same moments of order α and β, 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.





Autor: Stéphane Mischler - José Cañizo -

Fuente: https://hal.archives-ouvertes.fr/



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