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Publication 15-CNA-017
Pierre Degond Jian-Guo Liu Robert L. Pego Abstract: We study coagulation-fragmentation equations inspired by a
simple model
proposed in fisheries science to explain data for the size distribution of
schools of pelagic fish. Although the equations lack detailed balance and
admit no $H$-theorem, we are able to develop a rather complete
description of
equilibrium profiles and large-time behavior, based on recent
developments in
complex function theory for Bernstein and Pick functions. In the
large-population continuum limit, a scaling-invariant regime is reached in
which all equilibria are determined by a single scaling profile. This
universal
profile exhibits power-law behavior crossing over from exponent
$-\frac23$ for small
size to $-\frac32$ for large size, with an exponential cut-off.Get the paper in its entirety as 15-CNA-017.pdf |