A nonlinear parabolic system in the theory of combustion
Author:
D. H. Sattinger
Journal:
Quart. Appl. Math. 33 (1975), 47-61
MSC:
Primary 35B20; Secondary 35K60
DOI:
https://doi.org/10.1090/qam/463631
MathSciNet review:
463631
Full-text PDF Free Access
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D. A. Frank-Kamenetzky, Diffusion and heat exchange in chemical kinetics, translated by N. Thon, Princeton Univ. Press, Princeton, N. J., 1955
- Frank Hoppensteadt, On quasilinear parabolic equations with a small parameter, Comm. Pure Appl. Math. 24 (1971), 17–38. MR 269970, DOI https://doi.org/10.1002/cpa.3160240104
- Frank Hoppensteadt, Asymptotic series solutions of some nonlinear parabolic equations with a small parameter, Arch. Rational Mech. Anal. 35 (1969), 284–298. MR 248442, DOI https://doi.org/10.1007/BF00248163
- Frank Hoppensteadt, Properties of solutions of ordinary differential equations with small parameters, Comm. Pure Appl. Math. 24 (1971), 807–840. MR 288378, DOI https://doi.org/10.1002/cpa.3160240607
- Paul C. Fife, Singular perturbation problems whose degenerate forms have many solutions, Applicable Anal. 1 (1971/72), no. 4, 331–358. MR 296472, DOI https://doi.org/10.1080/00036817208839022
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- George R. Gavalas, Nonlinear differential equations of chemically reacting systems, Springer Tracts in Natural Philosophy, Vol. 17, Springer-Verlag New York Inc., New York, 1968. MR 0247815
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J. B. Keller, Perturbation theory, Six Lectures presented at MSU, Lansing, Michigan (1968)
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R. Aris, Introduction to the study of chemical reactors, Prentice-Hall, Englewood Cliffs, 1965 (1st edition)
D. R. Schneider, N. R. Amundson, and R. Aris, On a mechanism for autocatalysis, Chem. Eng. Sci. 27, 895–905 (1972)
D. A. Frank-Kamenetzky, Diffusion and heat exchange in chemical kinetics, translated by N. Thon, Princeton Univ. Press, Princeton, N. J., 1955
F. Hoppensteadt, On quasilinear parabolic equations with a small parameter, Comm. Pure Applied Math. 24, 17–38 (1971)
---, Asymptotic series solutions of some nonlinear parabolic equations with a small parameter Arch. Rat. Mech. Anal. 35 284–298 (1969)
---, Properties of solutions of ordinary differential equations with small parameters, Comm. Pure Appl. Math. 24 807–840 (1971)
P. Fife, Singular perturbation problems whose degenerate forms have many solutions, Applicable Analysis 1, 331–358 (1972)
I. M. Gelfand, Some problems in the theory of quasilinear equations, AHS Translations Ser. 2, 29, 295–381 (1963)
G. R. Gavalas, Nonlinear differential equations of chemically reacting systems, Springer, New York (1968)
J. R. Parks, Criticality criteria ... as functions of activation energy and temperature of assembly, J. Chem. Phys. 34, 46–50 (1961)
J. B. Keller, Perturbation theory, Six Lectures presented at MSU, Lansing, Michigan (1968)
S. Parter, Solutions of a differential equation arising in chemical reactor processes, Computer Sciences Dept. Univ. of Wisconsin, Technical Report #162, January 1973; SIAM J. Appl. Math. 26, 687–716 (1974)
M. H. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, (1967)
D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. Jour. 21, 979–1000 (1972)
D. H. Sattinger, Stability of solutions of nonlinear equations, Math. Anal. Appl. 39, 1–12 (1972)
R. Aris, Introduction to the study of chemical reactors, Prentice-Hall, Englewood Cliffs, 1965 (1st edition)
D. R. Schneider, N. R. Amundson, and R. Aris, On a mechanism for autocatalysis, Chem. Eng. Sci. 27, 895–905 (1972)
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Article copyright:
© Copyright 1975
American Mathematical Society
