zbMATH — the first resource for mathematics

Coagulation-fragmentation processes. (English) Zbl 0977.35060
This article studies some aspects of coagulation-fragmentation processes. In particular, the underlying mathematical foundations relating to the coagulation-fragmentation processes with cluster movement due to diffusion and superimposed transport processes are studied. The author deals with both the discrete version, where a countable system of coupled reaction-diffusion equations is considered and the continuous version, with an uncountable such system is studied.
The author proves that, under some conditions, a solution exists and is unique in the class of volume preserving solutions. This is achieved by interpreting the system as vector-valued parabolic evolution equations with the dependent variables taking values in infinite-dimensional Banach spaces.

35K57 Reaction-diffusion equations
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
Full Text: DOI