Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T12:03:52.500Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling silicosis: The structure of equilibria

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

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
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banasiak, J., Lamb, W. & Laurençot, P. (2019) Analytical Methods in Coagulation–Fragmentation Models, Vols. I and II, CRC Press, Boca Raton, London, New York.Google Scholar
da Costa, F. P. (2015) Mathematical aspects of coagulation-fragmentation equations. In: Bourguignon, J.-P., Jeltsch, R., Pinto, A. A. & Viana, M. (editors), Mathematics of Energy and Climate Change, Springer–Verlag, Cham, pp. 83–162.CrossRefGoogle Scholar
Flajolet, P., Gourdon, X. & Dumas, P. (1995) Mellin transforms and asymptotics: harmonic sums. Theor. Comp. Sci. 144, 3–58.CrossRefGoogle Scholar
Graham, R. L., Knuth, D. E. & Patashnik, P. (1994) Concrete Mathematics, 2nd ed., Addison Wesley, Reading, MA.Google Scholar
Pego, R. L. & Vélasquez, J. J. L. (2019) Temporal oscillations in Becker-Doering equations with atomization, arXiv:1905.02605 [math.DS].Google Scholar
Pinelis, I. (2004) L’Hôpital rules for monotonicity and the Wilker–Anglesio inequality. Am. Math. Monthly 111, 905–909.Google Scholar
Tran, C.-L., Jones, A. D. & Donaldson, K. (1995) Mathematical model of phagocytosis and inflammation after the inhalation of quartz at different concentrations. Scand. J. Work Environ. Health 21, 50–54.Google ScholarPubMed
Wattis, J. A. D. (2006) An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach. Physica D 222, 1–20.Google Scholar