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 |
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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 |
Publication status | Published - 2000 |