On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel

Breschi, G.
Fontelos, M. A.

Publication date

December 2022

Language

English

Abstract

We study the similarity solutions (SS) of Smoluchowski coagulation equation with multiplicative kernel $K(x,y)=(xy)^{s}$ for $s<\frac{1}{2}$. When $s<0$% , the SS consists of three regions with distinct asymptotic behaviours. The appropriate matching yields a global description of the solution consisting of a Gamma distribution tail, an intermediate region described by a lognormal distribution and a region of very fast decay of the solutions to zero near the origin. When $s\in \left( 0,\frac{1}{2}\right) $, the SS is unbounded at the origin. It also presents three regions: a Gamma distribution tail, an intermediate region of power-like (or Pareto distribution) decay and the region close to the origin where a singularity occurs. Finally, ful...

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On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel

Abstract

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On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel

Abstract

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