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Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems

Published online by Cambridge University Press:  14 November 2011

Nicholas D. Alikakos
Nicholas D. Alikakos
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Currie, Edinburgh EH14 4AS
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Synopsis

In §§1 and 2, we consider mainly a system of reaction-diffusion equations with general diffusion matrix and we establish the stabilization of all solutions at t →∞. The interest of this problem derives from two separate facts. First, the sets that are useful for localizing the asymptotics cease to be invariant as soon as the diffusion matrix is not a multiple of the identity. Second, the set of equilibria is connected. In §3, we establish uniform L§ bounds for the solutions of a class of parabolic systems. The unifying feature in the problems considered is the lack of any conventional maximum principles.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 265 - 286
Copyright
Copyright © Royal Society of Edinburgh 1983

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