Existence of solutions to coagulation-fragmentation systems with diffusion

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Abstract
We show existence of solutions to an infinite system of parabolic equations obtained by adding spatial diffusion to the classical coagulation-fragmentation equations. In the case where the spatial diffusion coefficients depend on cluster size, local existence is shown. A global solution is obtained in the case where all the diffusivities are equal. As done in previous studies on the coagulation-fragmentation system, the method of proof relies on the truncation of the infinite system; essential in the derivation of the necessary estimates is the fact that the total concentration of particles satisfies a parabolic equation, to which the maximum principle can be applied.