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

F. A. Davidson (Lead / Corresponding author), B. P. Rynne (Lead / Corresponding author)

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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 ≤ 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
    DOIs
    Publication statusPublished - Jun 2000

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