Discrete coagulation--fragmentation systems in weighted $\ell^1$ spaces
Functional Analysis
2026-02-19 v2
Abstract
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove existence, uniqueness and positivity of solutions of a corresponding semi-linear Cauchy problem in a weighted space. This requires the application of novel results, which we prove for abstract semi-linear Cauchy problems in Banach lattices where the non-linear term is defined only on a dense subspace.
Cite
@article{arxiv.2504.21665,
title = {Discrete coagulation--fragmentation systems in weighted $\ell^1$ spaces},
author = {Lyndsay Kerr and Matthias Langer},
journal= {arXiv preprint arXiv:2504.21665},
year = {2026}
}