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Maximum principles and comparison theorems for semilinear parabolic systems and their applications

Published online by Cambridge University Press:  14 November 2011

G. Lu  and
B. D. Sleeman
G. Lu
Affiliation:
Department of Mathematics and Computer Science, The University, Dundee DD1 4HN, Scotland
B. D. Sleeman
Affiliation:
Department of Mathematics and Computer Science, The University, Dundee DD1 4HN, Scotland
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Synopsis

A fundamental comparison theorem is established for general semilinear parabolic systems via the notions of sectorial operators, analytic semigroups and the application of the Tychonoff Fixed Point Theorem. Based on this result, we establish a maximum principle for systems of general parabolic operators and general comparison theorems for parabolic systems with quasimonotone or mixed quasimonotone nonlinearities. These results cover and extend most currently used forms of maximum principles and comparison theorems. A global existence theorem for parabolic systems is derived as an application which, in particular, gives rise to some global existence results for Fujita type systems and certain generalisations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 857 - 885
Copyright
Copyright © Royal Society of Edinburgh 1993

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