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Modelling silicosis: The structure of equilibria

Part of: Asymptotic theory Physiological, cellular and medical topics General theory in ordinary differential equations

Published online by Cambridge University Press:  31 October 2019

F. P. DA COSTA ,
M. DRMOTA  and
M. GRINFELD
F. P. DA COSTA
Affiliation:
Department of Science and Technology, Universidade Aberta, Rua da Escola Politécnica 141-7, P-1269-001 Lisboa, Portugal Centre for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, P-1049-001 Lisboa, Portugal e-mail: fcosta@uab.pt
M. DRMOTA
Affiliation:
Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstrasse 8-10/104, A-1040 Vienna, Austria e-mail: michael.drmota@tuwien.ac.at
M. GRINFELD
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK e-mail: m.grinfeld@strath.ac.uk
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Abstract

We analyse the structure of equilibria of a coagulation–fragmentation–death model of silicosis. We present exact multiplicity results in the particular case of piecewise constant coefficients, results on existence and non-existence of equilibria in the general case, as well as precise asymptotics for the infinite series that arise in the case of power law coefficients.

Keywords

Coagulation–fragmentation–death equationssilicosisasymptoticsMellin transform

MSC classification

Primary: 34A34: Nonlinear equations and systems, general
Secondary: 34E05: Asymptotic expansions 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 6 , December 2020 , pp. 950 - 967
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Copyright
© Cambridge University Press 2019

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References

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