Non-power law constant flux solutions for the Smoluchowski coagulation equation

TL;DR

This paper demonstrates the existence of non-power law solutions with constant mass flux in the Smoluchowski coagulation equation for certain kernels, expanding understanding beyond traditional power law solutions.

Contribution

It introduces new non-power law solutions with constant flux for the Smoluchowski equation using bifurcation methods, challenging previous assumptions.

Findings

Existence of non-power law solutions with constant flux

Bifurcation argument used to prove solutions

Expands understanding of solution types in coagulation equations

Abstract

It is well known that for a large class of coagulation kernels, Smoluchowski coagulation equations have particular power law solutions which yield a constant flux of mass along all scales of the system. In this paper, we prove that for some choices of the coagulation kernels there are solutions with a constant flux of mass along all scales which are not power laws. The result is proved by means of a bifurcation argument.