Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach

Wilson Lamb; Adam McBride; Louise Smith

doi:10.3934/dcds.2013.33.5177

Article Contents

2013, Volume 33, Issue 11&12: 5177-5187. Doi: 10.3934/dcds.2013.33.5177

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Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach

1.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH

Received: September 30, 2011

Revised: July 31, 2012

Published: October 2013

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Abstract

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators.

Keywords:

Semigroups of operators,
semilinear Cauchy problems,
multicomponent coagulation-fragmentation processes.

Mathematics Subject Classification: Primary: 47J35, 47D06; Secondary: 45K05, 80A30.

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