×

zbMATH — the first resource for mathematics

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

MSC:
35L65 Hyperbolic conservation laws
35F25 Initial value problems for nonlinear first-order PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.