Existence theorems for a free boundary problem in combustion theory
Authors:
Roberto Gianni and Paola Mannucci
Journal:
Quart. Appl. Math. 51 (1993), 43-53
MSC:
Primary 35R35; Secondary 35K57, 80A25
DOI:
https://doi.org/10.1090/qam/1205935
MathSciNet review:
MR1205935
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Additional Information
- J. Norbury and A. M. Stuart, A model for porous-medium combustion, Quart. J. Mech. Appl. Math. 42 (1989), no. 1, 159–178. MR 992797, DOI https://doi.org/10.1093/qjmam/42.1.159
- A. Fasano and M. Primicerio, Classical solutions of general two-phase parabolic free boundary problems in one dimension, Free boundary problems: theory and applications, Vol. I, II (Montecatini, 1981) Res. Notes in Math., vol. 78, Pitman, Boston, Mass.-London, 1983, pp. 644–657. MR 714939
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva, Lineĭ nye i kvazilineĭ nye uravneniya parabolicheskogo tipa, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0241821
- J. Norbury and A. M. Stuart, Parabolic free boundary problems arising in porous medium combustion, IMA J. Appl. Math. 39 (1987), no. 3, 241–257. MR 983744, DOI https://doi.org/10.1093/imamat/39.3.241
- Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
- J. Norbury and A. M. Stuart, Travelling combustion waves in a porous medium. I. Existence, SIAM J. Appl. Math. 48 (1988), no. 1, 155–169. MR 923295, DOI https://doi.org/10.1137/0148007
- J. Norbury and A. M. Stuart, Travelling combustion waves in a porous medium. II. Stability, SIAM J. Appl. Math. 48 (1988), no. 2, 374–392. MR 933040, DOI https://doi.org/10.1137/0148019
- David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications, Pure and Applied Mathematics, vol. 88, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 567696
- Avner Friedman and Athanassios E. Tzavaras, Combustion in a porous medium, SIAM J. Math. Anal. 19 (1988), no. 3, 509–519. MR 937466, DOI https://doi.org/10.1137/0519036
J. Norbury and A. M. Stuart, A model for porous medium combustion, Quart. J. Mech. Appl. Math. 42, 159–178 (1987)
A. Fasano and M. Primicerio, Classical solutions of general two-phase parabolic free boundary problems in one dimension, Free Boundary Problems: Theory and Applications, vol. II (A. Fasano and M. Primicerio, eds.), Pitman Advanced Publishing Program, Boston, London, and Melbourne, 1981
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Izdat. “Nauka", Moscow, 1967, Translations of Mathematical Monographs, Vol. 23, Amer. Math. Soc., Providence, RI, 1968
J. Norbury and A. M. Stuart, Parabolic free boundary problems arising in porous medium combustion, IMA J. Appl. Math. 39, 241–257 (1987)
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N.J., 1964
J. Norbury and A. M. Stuart, Travelling combustion waves in a porous medium. Part 1, Existence, SIAM J. Appl. Math. 48, 155–169 (1988)
J. Norbury and A. M. Stuart, Travelling combustion waves in a porous medium. Part 2, Stability, SIAM J. Appl. Math. 48, 374–392 (1988)
D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, New York, London, and Toronto, 1980
A. Friedman and A. Tzavaras, Combustion in a porous medium, SIAM J. Math. Anal. 19, 509–519 (1988)
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Article copyright:
© Copyright 1993
American Mathematical Society