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arXiv · 1704.01949

Uniqueness of fat-tailed self-similar profiles to Smoluchowski's coagulation equation for a perturbation of the constant kernel

Sebastian Throm
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Abstract

This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski's coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel $K$ which can be written as $K=2+\varepsilon W$. The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on $W$, we will show that for sufficiently small $\varepsilon$ there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile.

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Sebastian Throm. 2017-04-06. Uniqueness of fat-tailed self-similar profiles to Smoluchowski's coagulation equation for a perturbation of the constant kernel. https://arxiv.org/abs/1704.01949

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