Conservation laws and compensated compactness

  • Ronald J. DiPerna
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 195)


Generalize Entropy Hyperbolic System Admissible Solution Hyperbolic Setting Compressible Euler Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ball, J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337–403.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    DiPerna, R. J., Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), 27–70.ADSCrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    DiPerna, R. J., Convergence of the viscosity method for isentropic gas dynamics, to appear in Comm. Math. Phys.Google Scholar
  4. [4]
    DiPerna, R. J., Uniqueness of solutions to hyperbolic conservation laws, Indiana Univ. Math. J. 28 (1979), 137–188.CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697–715.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    Glimm, J. and P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Amer. Math. Soc. 101 (1970).Google Scholar
  7. [7]
    Friedrichs, K. O. and P. D. Lax, Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. USA (1971), 1686–1688.Google Scholar
  8. [8]
    Lax, P. D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537–566.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    Lax, P. D., Shock waves and entropy, in Contributions to Nonlinear Functional Analysis, ed. E. A. Zarantonello, Academic Press, 1971.Google Scholar
  10. [10]
    Murat, F., Compacité par compensation, Ann. Scuola Norm. Sup. Pisa 5 (1978), 489–507.Google Scholar
  11. [11]
    Tartar, L., Compensated compactness and applications to partial differential equations, in Research Notes in Mathematics, Nonlinear analysis and Mechanics: Heriot-Watt Symposium, Vol. 4, ed. R. J. Knops, Pitman Press (1979).Google Scholar
  12. [12]
    Tartar, L., The compensated compactness method applied to systems of conservation laws, in Systems of Nonlinear Partial Differential Equations, ed. J. M. Ball, NATO AS1 Series, D. Reidel Publishing Co. (1983).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Ronald J. DiPerna
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA

Personalised recommendations