Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
Publication 19-CNA-003
Jian-Guo Liu Barbara Niethammer Robert L. Pego Abstract: 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.Get the paper in its entirety as 19-CNA-003.pdf |