On the self-similar behavior of coagulation systems with injection

被引：2

作者：

Ferreira, Marina A. ^{[1
]}

Franco, Eugenia ^{[2
]}

Velazquez, Juan J. L. ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, POB 68, Helsinki 00014, Finland

[2] Univ Bonn, Inst Appl Math, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2023年 / 40卷 / 04期

基金：

欧洲研究理事会;

关键词：

Subject Classification; Primary Secondary; Self-similarity; Smoluchowski's coagulation equation; constant flux solutions; source term; moment bounds; FRAGMENTATION; EQUATION; DYNAMICS;

D O I：

10.4171/AIHPC/61

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-.YC3/= 2 as x-+ 0, where y < 1 is the homogeneity of the kernel, and are proven to decay at least exponentially as x-+ oo.

引用

页码：803 / 861

页数：59

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