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

2018/04/24 by Niethammer, Barbara, Nota, Alessia, Throm, Sebastian +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1804.08886

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^-σ. The validity of the equation has been rigorously proved in \citeNoV for values of the exponent σ>3. The solutions of this equation display a rich structure of different asymptotic behaviours according to the different values of the exponent σ. Here we show that for (5)/(3)

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