Optimal bounds for self-similar solutions to coagulation equations with product kernel

2010/10/09 by Niethammer, Barbara, Velazquez, Juan J. L.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.1857

Abstract

We consider mass-conserving self-similar solutions of Smoluchowski's coagulation equation with multiplicative kernel of homogeneity 2lλ∈ (0,1). We establish rigorously that such solutions exhibit a singular behavior of the form x^-(1+2λ) as x → 0. This property had been conjectured, but only weaker results had been available up to now.

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