Mass-conserving solutions to coagulation-fragmentation equations with nonintegrable fragment distribution function

Laurençot, Philippe

doi:10.1090/qam/1511

Author: Philippe Laurençot
Journal: Quart. Appl. Math. 76 (2018), 767-785
MSC (2010): Primary 45K05
DOI: https://doi.org/10.1090/qam/1511
Published electronically: June 26, 2018
MathSciNet review: 3855830
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Abstract: 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.

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