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Global a priori estimates for a viscous reactive gas*

Published online by Cambridge University Press:  14 November 2011

J. Bebernes  and
A. Bressan
J. Bebernes
Affiliation:
Department of Mathematics, University of Colorado, Boulder, CO 80309, U.S.A
A. Bressan
Affiliation:
Istituto di Matematica Applicata, Universita di Padova, 35100 Padova, Italy
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Synopsis

A priori estimates on the solution to the complete system of equations governing a heat-conductive, viscous reactive perfect gas confined between two infinite parallel plates are derived. From these estimates, global existence of both weak and classical solutions is obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 321 - 333
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1Bebernes, J. and Bressan, A.. Thermal behavior for a confined reactive gas. J. Differential Equations 44 (1982), 118–133.CrossRefGoogle Scholar
2Kassoy, D. and Poland, J.. The induction period of a thermal explosion in a gas between infinite parallel plates. Combustion and Flame 50 (1983), 259–274.Google Scholar
3Kazhikhov, A. V.. On the global solvability of one-dimensional boundary value problems for the equations of a viscous heat conducting gas (in Russian). In Dynamics of Continuous Medium, Ed. 24, 45–61 (Novosibirsk: Inst. Gidrodinamiki SO Akad. Nauk. SSSR, 1976).Google Scholar
4Kazhikhov, A. V. and Shelukhin, V. V.. The unique solvability in the large with respect to time of initial-boundary value problems for one-dimensional equations of viscous gas. J. Appl. Math. Mech. 41 (1977), 273–282.CrossRefGoogle Scholar
5Kazhikhov, A. V. and Solonnikov, V. A.. Existence theorems for the equations of motion of a compressible viscous fluid. Ann. Rev. Fluid Mech. 13 (1981), 79–95.Google Scholar
6Matsumura, A. and Nishida, T.. Initial-boundary value problems for the equations of motion of compressible viscous fluids. University of California Mathematical Sciences Research Institute, Technical Report, MSRI 008–83.Google Scholar
7Nash, J.. Le problème de Cauchy pour les equations differentielles d'un fluide general. Bull. Soc. Math. France 90 (1962), 487–497.CrossRefGoogle Scholar