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On the influence of the initial data in a combustion problem

Published online by Cambridge University Press:  17 February 2009

K. K. Tam
K. K. Tam
Affiliation:
Department of Mathematics, McGill University, Montreal Quebec H3C 3G1, Canada
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Abstract

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The combustion of a material can be modelled by two coupled parabolic partial differential equations for the temperature and concentration of the material. This paper deals with properties of the solution of these equations inside a cylinder or a sphere and under given initial conditions. Bounds for the variation of the temperature with the initial conditions are first established by considering a decoupled form of the equations. Then the coupled system is used to obtain approximate expressions for the temporal evolution of temperature and concentration.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 2 , October 1980 , pp. 193 - 209
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Duff, G. F. D. and Naylor, D., Differenrial equations of applied mathematics (Wiley, New York, 1966).Google Scholar
[2]Frank-Kamenetskii, D. A., Diffusion and heat transfer in chemical kinetics (Trans. ed. Appleton, J. P.) (Plenum Press, New York, 1969).Google Scholar
[3]Gelfand, I. M., “Some problems in the theory of quasi-linear equations”, Amer. Math. Soc. Trans. Ser. 2, 29 (1963), 295–381.Google Scholar
[4]Kassoy, D. R., “Extremely rapid transient phenomena in combustion, ignition and explosion”, in Asymptotic methods and singular perturbation (SIAM-AMS Proceedings, Vol. 10 1976).Google Scholar
[5]Parks, J. R., “Criticality criteria for various configurations of a self-heating chemical as functions of activation energy and temperature of assembly”, J. Chem. Phys. 34 (1961), 46–50.CrossRefGoogle Scholar
[6]Sattinger, D. H., “A nonlinear parabolic system in the theory of combustion”, Quart. of Appl. Math. 33 (1975), 47–61.CrossRefGoogle Scholar
[7]Tam, K. K., “Construction of upper and lower solutions for a problem in combustion theory” J. Math. Anal. Applic. 69 (1979), 131–145.CrossRefGoogle Scholar
[8]Tam, K. K., “Initial data and criticality for a problem in combustion theory”, J. Math. Anal. Applic. (to appear).Google Scholar