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Asymptotic behaviour of some reaction-diffusion systems modelling complex combustion on bounded domains

Published online by Cambridge University Press:  14 November 2011

Joel D. Avrin
Joel D. Avrin
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, U.S.A.
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Synopsis

We consider three models of multiple-step combustion processes on bounded spatial domains. Previously, steady-state convergence results have been established for these models with zero Neumann boundary conditions imposed on the temperature as well as the mass fractions. We retain here throughout the same boundary conditions on the mass fractions, but in our first set of results we establish steady-state convergence results with fixed Dirichlet boundary conditions on the temperature. Next, under certain physically reasonable assumptions, we develop, for two of the models, estimates on the decay rates of both mass fractions to zero, while for the remaining model we develop estimates on the decay rate of one concentration to zero and establish a positive lower bound on the other mass fraction. These results hold under either set of boundary conditions, but when the Dirichlet conditions are imposed on the temperature, we are able to obtain estimates on the rate of convergence of the temperature to its (generally nonconstant) steady-state. Finally, we improve the results of a previous paper by adding a temperature convergence result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1151 - 1163
Copyright
Copyright © Royal Society of Edinburgh 1993

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