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A note on the self-similar solutions to the spontaneous fragmentation equation
Giancarlo Breschi1, Marco A Fontelos1
1Instituto de Ciencias Matemáticas (ICMAT, CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera 15, 28049 Madrid, Spain.
Abstract:
We provide a method to compute self-similar solutions for various fragmentation equations and use it to compute their asymptotic behaviours. Our procedure is applied to specific cases: (i) the case of mitosis, where fragmentation results into two identical fragments, (ii) fragmentation limited to the formation of sufficiently large fragments, and (iii) processes with fragmentation kernel presenting a power-like behaviour.
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