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Existence and stability of solutions for semi-linear parabolic systems, and applications to some diffusion reaction equations

Published online by Cambridge University Press:  14 November 2011

Herbert Amann
Herbert Amann
Affiliation:
Mathematisches Institut, Ruhr-Universität, D-463, Bochum, Germany
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Synopsis

In this paper we study diffusion-reaction equations arising in the theory of chemical reactions. We prove the global existence and uniqueness of a solution without any restriction for the Lewis number and the Biot numbers. In addition, it is shown that there is at least one stationary state which is globally asymptotically stable (in a rather strong sense) provided the Thiele number is sufficiently small. These results are obtained as special cases from much more general results on semilinear parabolic systems, derived below.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 35 - 47
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

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