Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation

Abstract

An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non-negative, mass-conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving solution to the original non-autonomous coagulation and multiple-fragmentation equation.