A kinetic model for coagulation–fragmentation

Abstract

The aim of this paper is to show an existence theorem for a kinetic model of coagulation–fragmentation with initial data satisfying the natural physical bounds, and assumptions of finite number of particles and finite $L^p$-norm. We use the notion of renormalized solutions introduced by DiPerna and Lions (1989) [3], because of the lack of a priori estimates. The proof is based on weak-compactness methods in $L^1$, allowed by $L^p$-norms propagation.