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Invariants and asymptotic behavior of solutions of a conservation law. (English) Zbl 0392.35041

35L65 Hyperbolic conservation laws
35F25 Initial value problems for nonlinear first-order PDEs
Full Text: DOI
[1] Constantine M. Dafermos, Applications of the invariance principle for compact processes. II. Asymptotic behavior of solutions of a hyperbolic conservation law, J. Differential Equations 11 (1972), 416 – 424. · Zbl 0252.35045 · doi:10.1016/0022-0396(72)90055-1 · doi.org
[2] Ronald J. DiPerna, Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws, Indiana Univ. Math. J. 24 (1974/75), no. 11, 1047 – 1071. · Zbl 0309.35050 · doi:10.1512/iumj.1975.24.24088 · doi.org
[3] James Glimm and Peter D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Memoirs of the American Mathematical Society, No. 101, American Mathematical Society, Providence, R.I., 1970. · Zbl 0204.11304
[4] J. M. Greenberg and Donald D. M. Tong, Decay of periodic solutions of \partial \?/\partial \?+\partial \?(\?)/\partial \?=0, J. Math. Anal. Appl. 43 (1973), 56 – 71. · Zbl 0269.35011 · doi:10.1016/0022-247X(73)90257-6 · doi.org
[5] B. Keyfitz, Time-decreasing functionals of nonlinear conservation laws, Ph.D. thesis, New York Univ., 1970.
[6] P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537 – 566. · Zbl 0081.08803 · doi:10.1002/cpa.3160100406 · doi.org
[7] Peter D. Lax, Invariant functionals of nonlinear equations of evolution, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969), Univ. of Tokyo Press, Tokyo, 1970, pp. 240 – 251.
[8] O. A. Oleń≠nik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 165 – 170 (Russian).
[9] 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.
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