Discrete fragmentation equations with time-dependent coefficients

• DOI: 10.48550/arxiv.2212.10219
• Publication Date: 2024-01-01
• Authors: Kerr, Lyndsay; Lamb, Wilson; Langer, Matthias
• Keywords: Mathematics - Functional Analysis; 34G10, 47D06, 80A30, 34D05; FOS: Mathematics; 0101 mathematics; 01 natural sciences; Mathematics; 510; Functional Analysis (math.FA)

to appear in "Discrete and Continuous Dynamical Systems - Series S<br/>We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such discrete-size fragmentation models, we allow the fragmentation coefficients to vary with time. By formulating the initial-value problem for the system as a non-autonomous abstract Cauchy problem, posed in an appropriately weighted $\ell^1$ space, and then applying results from the theory of evolution families, we prove the existence and uniqueness of physically relevant, classical solutions for suitably constrained coefficients.<br/>