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arXiv · 1804.08886

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

Barbara Niethammer·Alessia Nota·Sebastian Throm·Juan J. L. Velázquez
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Abstract

In this paper we consider the long time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving at constant speed in a random distribution of fixed particles. The volumes $v$ of the particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{-\sigma}$. The validity of the equation has been rigorously proved in \cite{NoV} for values of the exponent $\sigma>3$. The solutions of this equation display a rich structure of different asymptotic behaviours according to the different values of the exponent $\sigma$. Here we show that for $\frac{5}{3}<\sigma<2$ the linear Smoluchowski equation is well posed and that there exists a unique self-similar profile which is asymptotically stable.

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Barbara Niethammer, Alessia Nota, Sebastian Throm, Juan J. L. Velázquez. 2018-04-24. Self-similar asymptotic behavior for the solutions of a linear coagulation equation. https://arxiv.org/abs/1804.08886

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