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Positivity for elliptic and parabolic systems

Published online by Cambridge University Press:  14 November 2011

J. F. G. Auchmuty
J. F. G. Auchmuty
Affiliation:
Fluid Mechanics Research Institute, University of Essex, and Department of Mathematics, Indiana University, Bloomington
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Synopsis

The positivity of solutions of initial-boundary value problems for weakly-coupled semilinear parabolic or elliptic systems of equations is studied. Conditions on the coupling terms are described which ensure that the solutions of the parabolic systems remain positive whenever the initial conditions are positive. For elliptic systems involving a parameter, conditions on the coupling terms are described which imply that solution branches which contain a positive solution, in fact, contain only positive solutions. Applications of these theorems to certain reaction-diffusion equations arising in the modelling of biological phenomena are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 3-4 , 1978 , pp. 183 - 191
Copyright
Copyright © Royal Society of Edinburgh 1978

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