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A singular Gierer—Meinhardt system with different source terms*

Published online by Cambridge University Press:  12 November 2008

Marius Ghergu  and
Vicenţiu Rădulescu
Marius Ghergu
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland and Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania ([email protected])
Vicenţiu Rădulescu
Affiliation:
Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania and Department of Mathematics, University of Craiova, 200585 Craiova, Romania ([email protected])
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Abstract

We study the existence and non-existence of classical solutions to a general Gierer—Meinhardt system with Dirichlet boundary condition. The main feature of this paper is that we are concerned with a model in which both the activator and the inhibitor have different sources given by general nonlinearities. Under some additional hypotheses and in the case of pure powers in nonlinearities, regularity and uniqueness of the solution in one dimension is also presented.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 6 , December 2008 , pp. 1215 - 1234
Copyright
Copyright © Royal Society of Edinburgh 2008

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References

* Dedicated to Professor Philippe G. Ciarlet on his 70th birthday.