Coagulation-fragmentation processes

• Published in: Archive for rational mechanics and analysis Vol. 151; no. 4; pp. 339 - 366
• Main Author: AMANN, H
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.04.2000; Berlin Springer Nature B.V; New York, NY
• Subjects: Coagulation; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fundamentals and general; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Particle dynamics; Physics; Rheology; Studies; Transport properties of condensed matter (nonelectronic); Parabolic equations; Particle motion; Coagulation; Cluster; Evolution equation; Numerical method; Diffusion; Reaction diffusion equation; Banach space; Fragmentation
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/s002050050200

We study the well-posedness of coagulation-fragmentation models with diffusion for large systems of particles. The continuous and the discrete case are considered simultaneously. In the discrete situation we are concerned with a countable system of coupled reaction-diffusion equations, whereas the continuous case amounts to an uncountable system of such equations. These problems can be handled by interpreting them as abstract vector-valued parabolic evolution equations, where the dependent variables take values in infinite-dimensional Banach spaces. Given suitable assumptions, we prove existence and uniqueness in the class of volume preserving solutions. We also derive sufficient conditions for global existence.[PUBLICATION ABSTRACT]