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

TY - JOUR

T1 - A priori bounds and global existence of solutions of the steady-state Sel'kov model

AU - Davidson, F. A.

AU - Rynne, B. P.

PY - 2000/6

Y1 - 2000/6

N2 - 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.

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.

U2 - 10.1017/S0308210500000275

DO - 10.1017/S0308210500000275

M3 - Article

SN - 0308-2105

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 -