期刊
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
卷 25, 期 -, 页码 553-578出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792514000126
关键词
Integral equations; Swarming patterns; Non-local problems; Bessel functions
资金
- Agencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya [MTM2011-27739-C04-02, 2009-SGR-345]
- Royal Society
- Engineering and Physical Sciences Research Council [EP/K008404/1]
- EPSRC [EP/K008404/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K008404/1] Funding Source: researchfish
We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise potential combining short-range repulsion and long-range attraction. We study particular solutions, which are referred to as flocks in the second-order models, for the specific choice of the Quasi-Morse interaction potential. Our main result is a rigorous analysis of continuous, compactly supported flock profiles for the biologically relevant parameter regime. Existence and uniqueness are proven for three space dimensions, while existence is shown for the two-dimensional case. Furthermore, we numerically investigate additional Morse-like interactions to complete the understanding of this class of potentials.
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