Transport processes with coagulation and strong fragmentation

Jacek Banasiak

doi:10.3934/dcdsb.2012.17.445

Article Contents

2012, Volume 17, Issue 2: 445-472. Doi: 10.3934/dcdsb.2012.17.445

This issue Previous Article Preface Next Article Compactness versus regularity in the calculus of variations

Transport processes with coagulation and strong fragmentation

Jacek Banasiak^1,

1.
School of Mathematical Sciences, University of KwaZulu-Natal, Durban

Received: June 30, 2010

Revised: November 30, 2010

Published: February 2012

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Abstract

In this paper we deal with equations describing fragmentation and coagulation processes with growth or decay, where the latter are modelled by first order transport equations. Our main interest lies in processes with strong fragmentation and thus we carry out the analysis in spaces ensuring that higher moments of the solution exist. We prove that the linear part, consisting of the transport and fragmentation terms, generates a strongly continuous semigroup in such spaces and characterize its generator as the closure of the sum (and in some cases the sum itself) of the operators describing the transport and fragmentation, defined on their natural domains. These results allow us to prove the existence of global in time strict solutions to the full nonlinear fragmentation-coagulation-transport equation.

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Mathematics Subject Classification: Primary: 35F25, 47D06; Secondary: 45K05, 80A30, 92D25.

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