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

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

2010-10-09

arxiv.org/abs/1010.1857v2

Mathematics

Analysis of PDEs

Scientific paper

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

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