On the self-similar behaviour of coagulation systems with injection

2021/06/23 by Ferreira, Marina A., Franco, Eugenia, Velázquez, Juan J. L.
#34A34 #45K05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2106.12421

Abstract

In this paper we prove the existence of a family of self-similar solutions for a class of coagulation equations with a constant flux of particles from the origin. These solutions are expected to describe the longtime asymptotics of Smoluchowski's coagulation equations with a time independent source of clusters concentrated in small sizes. The self-similar profiles are shown to be smooth, provided the coagulation kernel is also smooth. Moreover, the self-similar profiles are estimated from above and from below by x^-(γ+3)/2 as x → 0, where γ<1 is the homogeneity of the kernel, and are proven to decay at least exponentially as x → ∞.

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