Asymptotic formulas for the shock wave of the scalar conservation law with smooth initial data
Author:
Kazumi Tanuma
Journal:
Quart. Appl. Math. 50 (1992), 109-128
MSC:
Primary 35L67; Secondary 35L65, 76L05
DOI:
https://doi.org/10.1090/qam/1146627
MathSciNet review:
MR1146627
Full-text PDF Free Access
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Additional Information
- M. S. Berger and L. E. Fraenkel, On singular perturbations of nonlinear operator equations, Indiana Univ. Math. J. 20 (1970/71), 623–631. MR 271779, DOI https://doi.org/10.1512/iumj.1971.20.20050
- C. M. Dafermos, Characteristics in hyperbolic conservation laws. A study of the structure and the asymptotic behaviour of solutions, Nonlinear analysis and mechanics: Heriot-Watt Symposium (Edinburgh, 1976), Vol. I, Pitman, London, 1977, pp. 1–58. Res. Notes in Math., No. 17. MR 0481581
- John Guckenheimer, Solving a single conservation law, Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Springer, Berlin, 1975, pp. 108–134. Lecture Notes in Math., Vol. 468. MR 0606765
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M.S. Berger and L. E. Fraenkel, On singular perturbations of nonlinear operator equations, Indiana Univ. Math. J. 20 (7), 623–631 (1971)
C. M. Dafermos, Characteristics in hyperbolic conservation laws, Nonlinear Analysis and Mechanics, Vol. 1 (R. J. Knops, ed.), Pitman, London, 1977, pp. 1–58
G. Guckenheimer, Solving a single conservation law, Lecture Notes in Math., vol. 468, Springer-Verlag, New York, 1975, pp. 108–134
P. D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10, 537–566 (1957)
P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, CBMS, vol. 11, SIAM, Philadelphia, PA, 1973
D. G. Schaeffer, A regularity theorem for conservation laws, Adv. in Math. 11, 368–386 (1973)
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983
G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974
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Article copyright:
© Copyright 1992
American Mathematical Society
