Trend to steady state in a conservation law with spatial inhomogeneity
Author:
C. M. Dafermos
Journal:
Quart. Appl. Math. 45 (1987), 313-319
MSC:
Primary 35L65; Secondary 35L67, 76J99
DOI:
https://doi.org/10.1090/qam/895101
MathSciNet review:
895101
Full-text PDF Free Access
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Additional Information
- 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
- C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26 (1977), no. 6, 1097–1119. MR 457947, DOI https://doi.org/10.1512/iumj.1977.26.26088
- C. M. Dafermos, Large time behavior of solutions of hyperbolic balance laws, Bull. Soc. Math. Grèce (N.S.) 25 (1984), 15–29. MR 815565
- C. M. Dafermos, Regularity and large time behaviour of solutions of a conservation law without convexity, Proc. Roy. Soc. Edinburgh Sect. A 99 (1985), no. 3-4, 201–239. MR 785530, DOI https://doi.org/10.1017/S0308210500014256
- Gunilla Kreiss and Heinz-Otto Kreiss, Convergence to steady state of solutions of Burgers’ equation, Appl. Numer. Math. 2 (1986), no. 3-5, 161–179. MR 863984, DOI https://doi.org/10.1016/0168-9274%2886%2990026-7
- O. A. Oleĭnik, Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk (N.S.) 12 (1957), no. 3(75), 3–73 (Russian). MR 0094541
- M. D. Salas, S. Abarbanel, and D. Gottlieb, Multiple steady states for characteristic initial value problems, Appl. Numer. Math. 2 (1986), no. 3-5, 193–210. MR 863986, DOI https://doi.org/10.1016/0168-9274%2886%2990028-0
C. M. Dafermos, Characteristics in hyperbolic conservation laws, Nonlinear Analysis and Mechanics (R. J. Knops, Ed.), Research Notes in Math. No. 17, Pitman, London pp. 1–58, 1977
C. M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26, 1097–1119 (1977)
C. M. Dafermos, Large time behavior of solutions of hyperbolic balance laws, Bull. Greek Math. Soc. 25, 15–29 (1984)
C. M. Dafermos, Regularity and large time behavior of solutions of a conservation law without convexity, Proc. Royal Soc. Edinburgh 99A, 201–239 (1985)
G. Kreiss, and H. O. Kreiss, Convergence to steady state of solutions of Burgers’ equation, Appl. Num. Math. 2, 161–179 (1986)
O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspehi Mat. Nauk (N.S.) 12, 3–73 (1957). AMS Transl. Series 2, Vol. 26, pp. 95–172
M. D. Salas, S. Abarbanel, and D. Gottlieb, Multiple steady states for characteristic initial value problems, Appl. Num. Math. 2, 193–210 (1986).
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Article copyright:
© Copyright 1987
American Mathematical Society
