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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariants and asymptotic behavior of solutions of a conservation law
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by Tai Ping Liu PDF
Proc. Amer. Math. Soc. 71 (1978), 227-231 Request permission

Abstract:

We study the asymptotic behavior of solutions of the initial value problem for a conservation law ${u_t} + f{(u)_x} = 0$. It is assumed that the initial data agrees with the Riemann data for $|x|$ large. We show that the solution approaches that of the corresponding Riemann problem at algebraic rates.
References
  • 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. MR 296476, DOI 10.1016/0022-0396(72)90055-1
  • 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. MR 410110, DOI 10.1512/iumj.1975.24.24088
  • 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. MR 0265767
  • J. M. Greenberg and Donald D. M. Tong, Decay of periodic solutions of $\partial u/\partial t+\partial f(u)/\partial x=0$, J. Math. Anal. Appl. 43 (1973), 56–71. MR 320488, DOI 10.1016/0022-247X(73)90257-6
    • B. Keyfitz, Time-decreasing functionals of nonlinear conservation laws, Ph.D. thesis, New York Univ., 1970.
  • P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI 10.1002/cpa.3160100406
  • Peter D. Lax, Invariant functionals of nonlinear equations of evolution, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969) Univ. Tokyo Press, Tokyo, 1970, pp. 240–251. MR 0267254
  • O. A. Oleĭnik, 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). MR 0117408
  • 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, Res. Notes in Math., No. 17, Pitman, London, 1977, pp. 1–58. MR 0481581
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 227-231
  • MSC: Primary 35L67
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0500495-7
  • MathSciNet review: 500495