Growth–fragmentation–coagulation equations with unbounded coagulation kernels. (27th November 2020)

• Record Type: Journal Article
• Authors: Banasiak, J.; Lamb, W.
• Is Part Of: Philosophical transactions. Volume 378:Number 2185(2020)
• Publication Date: 2020-11-27
• Subjects: growth -- fragmentation and coagulation models -- C0-semigroups -- semilinear problems; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2019.0612
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : In this paper, we prove the global in time solvability of the continuous growth–fragmentation–coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool is the recently established result on moment regularization of the linear growth–fragmentation semigroup that allows us to consider coagulation kernels whose growth for large clusters is controlled by how good the regularization is, in a similar manner to the case when the semigroup is analytic. This article is part of the theme issue 'Semigroup applications everywhere'.