Open AccessMass-conserving solutions to coagulation-fragmentation equations with nonintegrable fragment distribution function
Author(s) -
Philippe Laurençot
Publication year - 2018
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1511
Subject(s) - fragmentation (computing) , singularity , coagulation , kernel (algebra) , fragment (logic) , mathematics , physics , mechanics , classical mechanics , mathematical analysis , pure mathematics , psychology , algorithm , psychiatry , computer science , operating system
Existence of mass-conserving weak solutions to the coagulation-fragmentation equation is established when the fragmentation mechanism produces an infinite number of fragments after splitting. The coagulation kernel is assumed to increase at most linearly for large sizes and no assumption is made on the growth of the overall fragmentation rate for large sizes. However, they are both required to vanish for small sizes at a rate which is prescribed by the (nonintegrable) singularity of the fragment distribution.