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A priori bounds and global existence of solutions of the steady-state Sel'kov model

Published online by Cambridge University Press:  11 July 2007

F. A. Davidson  and
B. P. Rynne
F. A. Davidson
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK (fdavidso@maths.dundee.ac.uk)
B. P. Rynne
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK (B.Rynne@ma.hw.ac.uk)
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Abstract

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We consider the system of reaction-diffusion equations known as the Sel'kov model. This model has been applied to various problems in chemistry and biology. We obtain a priori bounds on the size of the positive steady-state solutions of the system defined on bounded domains in Rn, 1 ≤ n ≤ 3 (this is the physically relevant case). Previously, such bounds had been obtained in the case n = 1 under more restrictive hypotheses. We also obtain regularity results on the smoothness of such solutions and show that non-trivial solutions exist for a wide range of parameter values.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 3 , June 2000 , pp. 507 - 516
Copyright
Copyright © Royal Society of Edinburgh 2000