Self-similar spreading in a merging-splitting model of animal group size
| Autor: | Barbara Niethammer, Jian-Guo Liu, Robert L. Pego |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Group (mathematics)
Zero (complex analysis) Statistical and Nonlinear Physics 45J05 70F45 92D50 37L15 44A10 35Q99 Sense (electronics) 01 natural sciences 010305 fluids & plasmas Nonlinear system Mathematics - Analysis of PDEs Distribution (mathematics) Animal groups Monotone polygon 0103 physical sciences Convergence (routing) FOS: Mathematics Statistical physics 010306 general physics Mathematical Physics Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1903.10020 |
| Popis: | In a recent study of certain merging-splitting models of animal-group size (Degond et al., J. Nonl. Sci. 27 (2017) 379), it was shown that an initial size distribution with infinite first moment leads to convergence to zero in weak sense, corresponding to unbounded growth of group size. In the present paper we show that for any such initial distribution with a power-law tail, the solution approaches a self-similar spreading form. A one-parameter family of such self-similar solutions exists, with densities that are completely monotone, having power-law behavior in both small and large size regimes, with different exponents. Comment: 27 pages |
| Databáze: | OpenAIRE |
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