Propagation of a combustion front in a striated solid medium: a homogenization analysis
Authors:
C.-M. Brauner, P. C. Fife, G. Namah and C. Schmidt-Lainé
Journal:
Quart. Appl. Math. 51 (1993), 467-493
MSC:
Primary 80A25; Secondary 35B27, 35K57
DOI:
https://doi.org/10.1090/qam/1233525
MathSciNet review:
MR1233525
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Abstract: A model problem for the propagation of a combustion front through a periodically inhomogeneous medium is posed. The existence of a steady state solution is proved, in which the front’s velocity is periodic in time. Computer simulations are carried out. Finally, through rigorous homogenization techniques, it is shown that when the wavelength of the inhomogeneity is small, the solution may be approximated by a travelling wave solution of the corresponding problem for a medium with certain constant properties.
M. Artola, Lectures on homogenization given at the University of Bordeaux I, 1986–1987
- Alain Bensoussan, Jacques-Louis Lions, and George Papanicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications, vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503330
- C.-M. Brauner and Cl. Schmidt-Lainé, Existence of a solution to a certain plane premixed flame problem with two-step kinetics, SIAM J. Math. Anal. 18 (1987), no. 5, 1406–1415. MR 902341, DOI https://doi.org/10.1137/0518102
- R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 0221256
J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969
- J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
M. Artola, Lectures on homogenization given at the University of Bordeaux I, 1986–1987
A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978
C. M. Brauner and Cl. Schmidt-Lainé, Existence of a solution to a certain plane premixed flame with 2-step kinetics, SIAM J. Math. Anal. 18, 1987
R. E. Edwards, Functional Analysis—Theory and Applications, Holt, Rinehart, and Winston, New York, 1965
J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969
J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vols. 1 et 2, Dunod, Paris, 1968
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Article copyright:
© Copyright 1993
American Mathematical Society