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

Philippe Laurençot (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 (non-integrable) singularity of the fragment distribution.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Philippe Laurençot. Mass-conserving solutions to coagulation-fragmentation equations with non-integrable fragment distribution function. Quarterly of Applied Mathematics, 2018, 76 (4), pp.767--785. ⟨10.1090/qam/1511⟩. ⟨hal-01773664⟩