Breschi G, Fontelos MA. A note on the self-similar solutions to the spontaneous fragmentation equation.
Proc Math Phys Eng Sci 2017;
473:20160740. [PMID:
28588398 DOI:
10.1098/rspa.2016.0740]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 04/10/2017] [Indexed: 11/12/2022] Open
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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