The fragmentation equation with size diffusion: Small and large size behavior of stationary solutions

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2021-05-21 DOI:10.3934/krm.2021032

Philippe Laurencçot, Christoph Walker

引用次数: 2

Abstract

The small and large size behavior of stationary solutions to the fragmentation equation with size diffusion is investigated. It is shown that these solutions behave like stretched exponentials for large sizes, the exponent in the exponential being solely given by the behavior of the overall fragmentation rate at infinity. In contrast, the small size behavior is partially governed by the daughter fragmentation distribution and is at most linear, with possibly non-algebraic behavior. Explicit solutions are also provided for particular fragmentation coefficients.

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具有粒径扩散的破碎方程:平稳解的大小粒径行为

研究了具有粒径扩散的破碎方程平稳解的大小尺寸行为。结果表明，这些解在大尺寸下表现为拉伸的指数，指数中的指数完全由无穷远处的整体破碎率的行为给出。相比之下，小尺寸的行为部分由子破碎分布控制，最多是线性的，可能具有非代数行为。给出了特定破碎系数的显式解。

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

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.