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

Authors: Davidson F.A.; Rynne B.P.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 130, Number 3, 4 June 2000 , pp. 507-516(10)

Publisher: Royal Society of Edinburgh

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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 Rⁿ, 1

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.

Document Type: Research article

Publication date: 2000-06-04