具有多项式子碎片分布的破碎方程自相似解的稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-12-27 DOI:10.3934/krm.2023016

M. Fontelos

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引用次数: 0

摘要

我们研究了具有幂律破碎率和多项式子碎片分布函数$p(s)$的破碎方程。分析了相应的自相似解，并推导了它们的指数衰减渐近性质和$C^{\infty }$正则性。证明了自相似解(在光滑指数衰减摄动下)随时间的急剧指数衰减率的稳定性，以及$t>0$解的$C^{\infty }$规律性。结果是基于广义拉盖尔多项式的显式展开式和对这种展开式的分析。对于无穷远处幂律衰减的扰动，也证明了其稳定性。最后，我们考虑实解析$p(s)$。

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Stability of selfsimilar solutions to the fragmentation equation with polynomial daughter fragments distribution

We study fragmentation equations with power-law fragmentation rates and polynomial daughter fragments distribution function $p(s)$. The corresponding selfsimillar solutions are analysed and their exponentially decaying asymptotic behaviour and $C^{\infty }$ regularity deduced. Stability of selfsimilar solutions (under smooth exponentially decaying perturbations), with sharp exponential decay rates in time are proved, as well as $C^{\infty }$ regularity of solutions for $t>0$. The results are based on explicit expansion in terms of generalized Laguerre polynomials and the analysis of such expansions. For perturbations with power-law decay at infinity stability is also proved. Finally, we consider real analytic $p(s)$.

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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.