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Shocks violating Lax's condition are unstable


Authors: E. D. Conway and J. A. Smoller
Journal: Proc. Amer. Math. Soc. 39 (1973), 353-356
MSC: Primary 35L65
DOI: https://doi.org/10.1090/S0002-9939-1973-0430545-3
MathSciNet review: 0430545
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Abstract: For a system of two conservation laws, we prove that solutions violating Lax's condition across shocks are unstable relative to smoothing of the initial data.


References [Enhancements On Off] (What's this?)

  • [1] J. Glimm and P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc. No. 101 (1970). MR 42 #676. MR 0265767 (42:676)
  • [2] J. L. Johnson, Global continuous solutions of hyperbolic systems of quasi-linear equations, Bull. Amer. Math. Soc. 73 (1967), 639-641. MR 35 #4593. MR 0213735 (35:4593)
  • [3] P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 20 #176. MR 0093653 (20:176)
  • [4] J. A. Smoller and J. L. Johnson, Global solutions for an extended class of hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 32 (1969), 169-189; Erratum, ibid. 37 (1970), 399-400. MR 38 #4822; MR 41 #645. MR 0236527 (38:4822)
  • [5] M. Yamaguti and T. Nishida, On some global solution for quasi linear hyperbolic equations, Funkcial. Ekvac. 11 (1968), 51-57. MR 39 #634. MR 0239277 (39:634)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0430545-3
Article copyright: © Copyright 1973 American Mathematical Society

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