On the self-similar behavior of coagulation systems with injection

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-23 DOI:10.4171/aihpc/61

Marina A. Ferreira, Eugenia Franco, J. Vel'azquez

引用次数: 5

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 $x^{-(\gamma+3)/2}$ as $x \to 0$, where $\gamma<1 $ is the homogeneity of the kernel, and are proven to decay at least exponentially as $x \to \infty$.

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注射型混凝体系的自相似行为

本文证明了一类从原点出发具有恒定粒子通量的凝聚方程的一类自相似解的存在性。这些解有望描述具有时间无关的小尺寸聚集源的Smoluchowski凝聚方程的长期渐近性。如果凝聚核也是光滑的，则自相似轮廓是光滑的。此外，自相似的轮廓从上到下由$x^{-(\gamma+3)/2}$估计为$x \to 0$，其中$\gamma<1 $是内核的同质性，并且被证明至少呈指数衰减为$x \to \infty$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.