Weak solutions to the Cauchy problem for the diffusive discrete coagulation–fragmentation system

The initial value problem for the discrete coagulation–fragmentation system with diffusion is studied. This is an infinite countable system of reaction–diffusion equations describing coagulation and fragmentation of discrete clusters moving by spatial diffusion in all space Rd . The model considered in this work is a generalization of Smoluchowski’s discrete coagulation equations. Existence of global-in-time weak solutions to the Cauchy problem is proved under natural assumptions on initial data for unbounded coagulation and fragmentation coefficients. This work extends existence theory for this system from the case of clusters distribution on bounded domain subject to no-flux boundary condition to the case of all Rd .  2003 Elsevier Inc. All rights reserved.