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Hyperbolic systems of conservation laws with some special invariance properties

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Abstract

The Euler equations of fluid dynamics are an example of a very special class of nonlinear, hyperbolic systems of conservation laws, in particular those satisfying conditions of reflection and Galilean invariance. These invariance properties are directly responsible for several of the attractive structural features of this system.

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References

  1. P. D. Lax,Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math.10(1957), 537–566.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. D. Lax,Shock waves and entropy, inContradictions to Nonlinear Functional Analysis (E. Zarontonello, ed.), Academic Press, New York, 1971.

    Google Scholar 

  3. T. P. Liu,The Riemann problem for general systems of conservation laws, J. Differ. Equ.18 (1975), 218–234.

    Article  MATH  Google Scholar 

  4. T. P. Liu,The entropy condition and admissibility of shocks, J. Math. Anal. Appl.53 (1976), 78–88.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Majda,The stability of multi-dimensional shock fronts, AMS Memoirs 275 (1983).

  6. M. S. Mock,Discrete shocks and genuine nonlinearity, Michigan Math. J.25 (1978), 131–146.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Schochet,Stability of a large shock under small BV perturbations (to appear).

  8. M. Sever,Existence in the large for Riemann problems for systems of conservation laws, Trans. Amer. Math. Soc.292(1985), 375–381.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Smith,The Riemann problem in gas dynamics, Trans. Amer. Math. Soc.249 (1979), 1–50.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Smoller,Shock Waves and Reaction — Diffusion Equations, Springer-Verlag, New York/Berlin, 1983.

    MATH  Google Scholar 

  11. G. B. Whitham,Linear and Nonlinear Waves, Wiley, New York, 1974.

    MATH  Google Scholar 

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Sever, M. Hyperbolic systems of conservation laws with some special invariance properties. Israel J. Math. 75, 81–104 (1991). https://doi.org/10.1007/BF02787183

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  • DOI: https://doi.org/10.1007/BF02787183

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