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On $ L\sb 1$-contraction for systems of conservation laws


Author: Jorge G. S. Patiño
Journal: Proc. Amer. Math. Soc. 101 (1987), 465-469
MSC: Primary 35L65
DOI: https://doi.org/10.1090/S0002-9939-1987-0908650-4
MathSciNet review: 908650
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Abstract: We prove that for $ 2 \times 2$, strictly hyperbolic, genuinely nonlinear systems of conservation laws, there is no metric $ D$ such that

$\displaystyle \int_{ - \infty }^\infty {D(u(x,t),c)dx} $

is a nonincreasing function of time for every weak solution $ u,{u_0}( \pm \infty ) = c$.

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

  • [1] P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 19 (1957), 537-566. MR 0093653 (20:176)
  • [2] J. B. Temple, No $ {L_1}$-contractive metrics for systems of conservation laws, Trans. Amer. Math. Soc. 288 (1985), 471-480. MR 776388 (86h:35084)
  • [3] -, Decay with a rate for noncompactly supported solutions of conservation laws, Trans. Amer. Math. Soc. 298 (1986), 43-82. MR 857433 (87k:35163)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0908650-4
Keywords: Conservation laws, decay of solutions, $ {L_1}$-dependence
Article copyright: © Copyright 1987 American Mathematical Society

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