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Entropy and the stability of classical solutions of hyperbolic systems of conservation laws

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1640)

Keywords

Weak Solution Compact Subset Classical Solution Hyperbolic System Entropy Inequality 
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.

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References

  1. [B] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977), 337–403.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [B1] G. Boillat, Sur l’ existence et la recherche d’ équations de conservation supplémentaires pour les systèmes hyperboliques. C.R. Acad. Sc. Paris 278 (1974), 909.MathSciNetzbMATHGoogle Scholar
  3. [B2] G. Boillat, Involutions des systèmes conservatifs. C.R. Acad. Sc. Paris 307 (1988), 891–894.MathSciNetzbMATHGoogle Scholar
  4. [D] B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals. Lecture Notes in Math. No. 922. Berlin: Springer-Verlag 1982.CrossRefzbMATHGoogle Scholar
  5. [Da] C.M. Dafermos, Quasilinear hyperbolic systems with involutions. Arch. Rat. Mech. Anal. 94 (1986), 373–389.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [Di] R.J. DiPerna, Uniqueness of solutions to hyperbolic conservation laws. Indiana U. Math. J. 28 (1979), 137–188.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [FL] K.O. Friedrichs and P.D. Lax, Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. USA 68 (1971), 1686–1688.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [G] S.K. Godunov, An interesting class of quasilinear systems. Sov. Math. 2 (1961), 947–948.zbMATHGoogle Scholar
  9. [M] A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. New York: Springer-Verlag 1984.CrossRefzbMATHGoogle Scholar
  10. [Mo] C.B. Morrey, Quasiconvexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952), 25–53.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [RS] T. Ruggeri and A. Strumia, Main field and convex covariant density for quasilinear hyperbolic systems. Ann. Inst. Henri Poincaré. 34 (1981), 65–84.MathSciNetzbMATHGoogle Scholar
  12. [S] V. Šverák Rank-one convexity does not imply quasicovexity. Proc. Roy. Soc. Edinburgh 120 (1992), 185–189.CrossRefzbMATHGoogle Scholar
  13. [TN] C. Truesdell, and W. Noll, The Nonlinear Field Theories of Mechanics. Handbuch der Physik III/3, ed. S. Flügge. Berlin: Springer-Verlag 1965.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  1. 1.Lefschetz Center for Dynamical SystemsBrown UniversityProvidenceUSA

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