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

Philippe Laurençot; Christoph Walker

doi:10.3934/krm.2021032

Article Contents

2021, Volume 14, Issue 6: 961-980. Doi: 10.3934/krm.2021032

This issue Previous Article Relativistic BGK model for massless particles in the FLRW spacetime Next Article Macroscopic descriptions of follower-leader systems

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

Philippe Laurençot^1, and
Christoph Walker^2,

1.
Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, F–31062 Toulouse Cedex 9, France
2.
Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover, Germany

Received: May 2021

Revised: September 2021

Early access: November 2021

Published: December 2021

The first author is partially supported by Deutscher Akademischer Austauschdienst funding programme Research Stays for University Academics and Scientists, 2021 (57552334)

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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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Mathematics Subject Classification: Primary: 45K05.

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References

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