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Existence of solutions to coagulation-fragmentation systems with diffusion. (English) Zbl 0870.35117
Summary: 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 the 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 derivative 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.

MSC:
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
35K57 Reaction-diffusion equations
82D60 Statistical mechanics of polymers
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