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arXiv · 1010.1857

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

Barbara Niethammer·Juan J. L. Velazquez
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Abstract

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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Barbara Niethammer, Juan J. L. Velazquez. 2010-10-09. Optimal bounds for self-similar solutions to coagulation equations with product kernel. https://arxiv.org/abs/1010.1857

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