FRAGMENTATION-DIFFUSION MODEL - EXISTENCE OF SOLUTIONS AND THEIR ASYMPTOTIC-BEHAVIOR

An infinite system of reaction-diffusion equations that represents a p articular case of the discrete coagulation-fragmentation model with di ffusion is studied. The reaction part of the model describes the rate of clusters break-up into smaller particles. Diffusion constants are a ssumed to be different in each equation and concentration-dependent fr agmentation coefficients are considered. Existence of solutions is stu died under fairly general assumptions on fragmentation coefficients an d initial data Uniqueness in the class of mass-preserving solutions is proved. Convergence of solutions to spatially homogeneous equilibrium state is obtained.