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

F. A. Davidson, B. P. Rynne

Research output: Contribution to journalArticle

43 Citations (Scopus)

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 = 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.

Original languageEnglish
Pages (from-to)507-516
Number of pages10
JournalProceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume130
Issue number3
Publication statusPublished - 2000

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