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Existence and uniqueness of stationary solutions of some reaction–diffusion equations arising in chemical reactor kinetics

Published online by Cambridge University Press:  14 November 2011

Jörg Swetina
Jörg Swetina
Affiliation:
Institut für theoretische Chemie und Strahlenchemie der Universität Wien, Währingerstrasse 17, A-1090 Wien, Austria
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Synopsis

In this paper we give a proof on existence of non-negative solutions of weakly coupled systems of non-linear elliptic PDE's which model isothermal chemical reactions in a bounded volume Ω. The boundaries of this “diffusion reactor” will be allowed to be differently permeable to different species, giving rise to homogeneous Neumann, or inhomogeneous mixed, boundary conditions. We assume a “conservation of mass” condition and a second condition, the choice of which is motivated in an example.

In the second section we prove that the PDE system that describes the reaction:

in the diffusion reactor admits a unique stationary solution.

For this proof we must show invertibility for a class of non inverse-positive linear elliptic operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 249 - 263
Copyright
Copyright © Royal Society of Edinburgh 1989

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