### 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 R^{n}, 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 |

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## Cite this

Davidson, F. A., & Rynne, B. P. (2000). A priori bounds and global existence of solutions of the steady-state Sel'kov model.

*Proceedings of the Royal Society of Edinburgh, Section A: Mathematics*,*130*(3), 507-516.