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Can hyperbolic systems of conservation laws be well-posed in BV(R;RN)?

  • Hyperbolic P.D.E. Theory
  • Conference paper
  • First Online:
Nonlinear Hyperbolic Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1270))

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Abstract

The solution of a hyperbolic system of conservation laws is bounded in BV in terms of the BV norms of its initial data. It depends continuously on its initial data, if an appropriate distance in BV is defined. These results hold on piecewise smooth solutions satisfying the entropy condition.

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References

  1. P. Benilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thèse de doctorat d'Etat, Orsay 1971

    Google Scholar 

  2. M.G. Crandall, The semi-group approach to first order quasilinear equations in several space variables, Israel J. Math. 12(1972)108–132.

    Article  MathSciNet  MATH  Google Scholar 

  3. R.J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82(1983)27–70.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Glimm, Solutions in the large for nonlinear systems of conservation laws, Comm. Pure Appl. Math. 18(1965)685–715.

    Article  MathSciNet  Google Scholar 

  5. M. Golubitsky, D.G. Schaeffer, Stability of shock waves for a single conservation law, Advances in Math. 16(1975)65–71.

    Article  MathSciNet  MATH  Google Scholar 

  6. S.N. Kruzhkov, first order quasilinear equations with several independant variables, Mat. Sb. (NS) 81(123)(1970)228–255 = Math. USSR Sb 10(1970) 217–243.

    Google Scholar 

  7. P.D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10(1957)537–556.

    Article  MathSciNet  MATH  Google Scholar 

  8. P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, C.B.M.S. S.I.A.M. Philadelphie, 1973.

    Google Scholar 

  9. O.A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspehi Mat. Nauk, 12(1957)3(75)3–73 = AMS Transl. (2)26(1963)95–172.

    MathSciNet  Google Scholar 

  10. B. Quinn, solutions with shocks: An example of L1 contractive semi-groups, Comm. Pure Appl. Math. 24(1971)125–132.

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Schaeffer, A regularity theorem for conservation laws, Advances in Math. 11(1973)368–386.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Schatzman, Continuous Glimm functionals and uniqueness of solutions of Riemann problem, Indiana Univ. Math. J., 34(1985)533–589.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Schatzman, The geometry of continuous Glimm functionals, A.M.S. Lectures Appl. Math.,23(1986)417–439.

    MathSciNet  MATH  Google Scholar 

  14. B. Temple, this conference.

    Google Scholar 

  15. A.I. Vol'pert, The space BV and quasilinear equations, Math. USSR Sb. 21(1967)225–267

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathématiques, Université Claude-Bernard, 69622, Villeurbanne Cedex, France

    Michelle Schatzman

Authors
  1. Michelle Schatzman
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Editor information

Claude Carasso Denis Serre Pierre-Arnaud Raviart

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© 1987 Springer-Verlag

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Schatzman, M. (1987). Can hyperbolic systems of conservation laws be well-posed in BV(R;RN)?. In: Carasso, C., Serre, D., Raviart, PA. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078333

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  • DOI: https://doi.org/10.1007/BFb0078333

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18200-9

  • Online ISBN: 978-3-540-47805-8

  • eBook Packages: Springer Book Archive

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