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

F. A. Davidson; B. P. Rynne

doi:10.1017/S0308210500000275

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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57 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 language	English
Pages (from-to)	507-516
Number of pages	10
Journal	Proceedings of the Royal Society of Edinburgh, Section A : Mathematics
Volume	130
Issue number	3
DOIs	https://doi.org/10.1017/S0308210500000275
Publication status	Published - Jun 2000

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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.",

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AU - Rynne, B. P.

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AB - 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.

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DO - 10.1017/S0308210500000275

M3 - Article

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VL - 130

SP - 507

EP - 516

JO - Proceedings of the Royal Society of Edinburgh, Section A : Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A : Mathematics

IS - 3

ER -

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

Abstract

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