Heriot-Watt Mathematics Report Series
HWM97-33, 22 October 1997

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

FA Davidson and BP Rynne


Abstract

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 $\R^n$, $1 \le n \le 3$ (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.

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Full text: http://www.ma.hw.ac.uk/~bryan/ps_files/bounds.ps.Z


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