Details
| Original language | English |
|---|---|
| Pages (from-to) | 961–980 |
| Number of pages | 20 |
| Journal | Kinetic and Related Models |
| Volume | 14 |
| Issue number | 6 |
| Early online date | Nov 2021 |
| Publication status | Published - Dec 2021 |
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.
Keywords
- Fragmentation, asymptotics, size diffusion, stationary solution
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
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In: Kinetic and Related Models, Vol. 14, No. 6, 12.2021, p. 961–980.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Fragmentation Equation with Size Diffusion: Small and Large Size Behavior of Stationary Solutions
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding Information: This work was done while PhL enjoyed the kind hospitality of the Institut f?r Angewandte Mathematik, Leibniz Universit?t Hannover. We thank the referees for helpful remarks. Funding Information: 2020 Mathematics Subject Classification. Primary: 45K05. Key words and phrases. Fragmentation, size diffusion, stationary solution, asymptotics. The first author is partially supported by Deutscher Akademischer Austauschdienst funding programme Research Stays for University Academics and Scientists, 2021 (57552334).
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Fragmentation
KW - asymptotics
KW - size diffusion
KW - stationary solution
UR - http://www.scopus.com/inward/record.url?scp=85121379822&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2105.10166
DO - 10.48550/arXiv.2105.10166
M3 - Article
VL - 14
SP - 961
EP - 980
JO - Kinetic and Related Models
JF - Kinetic and Related Models
SN - 1937-5093
IS - 6
ER -