EXISTENCE AND UNIQUENESS RESULTS FOR THE NONAUTONOMOUS COAGULATION AND MULTIPLE-FRAGMENTATION EQUATION

An initial-value problem modelling coagulation and fragmentation proce sses 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 co ntraction mapping principle. A unique global, nonnegative, mass-conser ving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving s olution to the original non-autonomous coagulation and multiple-fragme ntation equation. (C) 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.