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Stability of Multi-Dimensional Weak Shocks

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Multidimensional Hyperbolic Problems and Computations

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 29))

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Abstract

In this paper we discuss the stability of weak shocks for a class of multi-dimensional systems of conservation laws, containing Euler’s equations of gas dynamics; we study the well-posedness of the linearized problem, and study the behaviour of the L 2 estimates when the strength of the shock approaches zero.

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References

  1. S. Alinhac, Existence d’ondes de raréfaction pour des systèmes quasilinéaires multidimensionnels, Comm. in Partial Diff. Equ., 14 (1989), pp. 173–230.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sc. E.N.S., 14 (1981), pp. 209–246.

    MathSciNet  MATH  Google Scholar 

  3. J. Chazarain — A. Piriou, Introduction à la théorie des équations aux dérivées partielles, Bordas (Dunod), Paris, 1981, English translation Studies in Math, and its Applications, vol 14, North Holland (1982).

    Google Scholar 

  4. R. Coifman — Y. Meyer, Au delà des opérateurs pseudodifférentiels, Astérisque 57 (1978).

    Google Scholar 

  5. H.O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure and Appl. Math., 23 (1970), pp. 277–298.

    Article  MathSciNet  Google Scholar 

  6. P. Lax, Hyperbolic systems of conservation laws, Comm. on Pure and Appl. Math., 10 (1957), pp. 537–566.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Majda, The stability of multidimensional shock fronts, Memoirs of the Amer. Math. Soc., n° 275 (1983).

    Google Scholar 

  8. A. Majda, The existence of multidimensional shock fronts, Memoirs of the Amer. Math. Soc, n° 281 (1983).

    Google Scholar 

  9. G. Métivier, Interaction de deux chocs pour un système de deux lois de conservation en dimension deux d’espace, Trans. Amer. Math. Soc, 296 (1986), pp. 431–479.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. Métivier, Ondes soniques, Séminaire E.D.P. École Polytechnique, année 1987–88, exposé n° 17 & preprint à paraitre, J. Math. Pures et Appl..

    Google Scholar 

  11. G. Métivier, Stability of weak shocks, preprint.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IRMAR URA 0305 CNRS, Université de Rennes I, Campus Beaulieu, 35042, Rennes Cedex, France

    Guy Métivier

Authors
  1. Guy Métivier
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY, 11794-3600, USA

    James Glimm

  2. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Andrew J. Majda

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© 1991 Springer-Verlag New York, Inc.

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Métivier, G. (1991). Stability of Multi-Dimensional Weak Shocks. In: Glimm, J., Majda, A.J. (eds) Multidimensional Hyperbolic Problems and Computations. The IMA Volumes in Mathematics and Its Applications, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9121-0_19

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  • DOI: https://doi.org/10.1007/978-1-4613-9121-0_19

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9123-4

  • Online ISBN: 978-1-4613-9121-0

  • eBook Packages: Springer Book Archive

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