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Free boundary value problems associated with the growth and development of multicellular spheroids

Published online by Cambridge University Press:  01 December 1997

H. M. BYRNE  and
M. A. J. CHAPLAIN
H. M. BYRNE
Affiliation:
Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK (email: h.byrne@umist.ac.uk)
M. A. J. CHAPLAIN
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, UK (email: Chaplain@mcs.dundee.ac.uk)
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Abstract

In this paper a generalized model for the growth of avascular tumours is presented. The formulation leads naturally to the incorporation of free boundaries which define the outer tumour surface explicitly and various inner surfaces implicitly. A combination of numerical simulations, asymptotic analysis and perturbation techniques is used to study the model and yields results, which agree well with experimentally-observed phenomena.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 6 , December 1997 , pp. 639 - 658
Copyright
1997 Cambridge University Press

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