Advertisement

Introduction Aux Problemes Hyperboliques Non Lineaires

  • C. Bardos
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1047)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. [1]
    P. COLELLA, GLIMM: Methods for Gaz Dynamic, SIAM Journal on Scientific an-Statistical Compating, Vol 3, pp. 76–110 (1982).CrossRefGoogle Scholar
  2. [2]
    J. CONLON and T.P. LIU: Admissibility criteria for hyperbolic conservation Law. Indiana Univ. Math. J 30 (1981) 5, pp. 641–652.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    E.D. CONWAY et J.S. SMOLLER: Global solution of the Cauchy problem for quasilinear first order equation in several space variables. Comm. Pure Appl. Math. 19 (1966), pp. 95–105.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    A.J. CHORIN: Random Choice Solution of Hyperbolic System. Journ. of Comp. Phys. 22, 2 (1976), pp. 517–533.ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A.J. CHORIN: Random Choice Methods with applications to Reaction Gas Flow, Journ. of Comp. Phys. 25, 3 (1977), pp. 253–272.ADSCrossRefMATHGoogle Scholar
  6. [6]
    K.N. CHUEH, C.C. CONLEY et J. SMOLLER: Positively invariant Regions for systems of non linear Diffusion Equation. Indiana University Math. Jour. 26, 2 (1977), pp. 373–391.CrossRefMATHGoogle Scholar
  7. [7]
    M.G. CRANDALL et T.M. LIGGETT: Generation of semi groups of non linear transformations on general Banach Spaces, Amer. J. Math. 93 (1971), pp. 265–298.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    C. DAFERMOS: The entropy rate admissibility criteria for solutions of hyperbolic conservation Laws. Journ. of Diff. Equations, 14, 2 (1973), pp. 202–212.ADSCrossRefMATHGoogle Scholar
  9. [9]
    M. Da VEIGA et A. VALLI: On the motion of a non homogeneous ideal incompressible fluid in an external force field, Rend. Sem. Math. Univ. Padova, vol 159, (1978), pp. 115–145.MATHGoogle Scholar
  10. [10]
    R. Di PERNA: Uniqueness of Solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 28 (1979), pp. 137–187.MathSciNetCrossRefGoogle Scholar
  11. [11]
    R. Di PERNA: à paraître aux Archiv for Mech. and Analysis (1983).Google Scholar
  12. [12]
    K.O. FRIEDRICHS et P.D. LAX: Systems of Conservation Equation with a convex Extension. Proc. Nat. Acad. Sci. U.S.A., 68, 8 (1971), pp. 1686–1688.ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    J. GLIMM: Solution in the large for non linear hyperbolic systèmes of equations. Comm. Pure Apl. Math. 18 (1965), pp. 697–715.CrossRefMATHGoogle Scholar
  14. [14]
    GOLUBITZKY et D. SCHAEFFER: Stability of schock waves for a single conservation law. Advances in Math. 16 (1975) pp. 65–71.MathSciNetCrossRefGoogle Scholar
  15. [15]
    D. HOPF: A characterisation of the blow uptime for the solution of a conservation law in several space variable. Comm. in Partial Diff. Equations, 7, 2 (1982), pp. 141–151.CrossRefGoogle Scholar
  16. [16]
    E. HOPF: The partial differential equation ut+uux=uxx, Comm. Pure App. Math. 3 (1950), pp. 201–230.CrossRefGoogle Scholar
  17. [17]
    T. KATO: The Cauchy Problem for quasilinear Symmetric Hyperbolic Systems Ard. Pub. Mech. and Anal., 58, 3 (1975), pp. 181–205.MATHGoogle Scholar
  18. [18]
    S. KLAINERMAN et A. MAJDA: Singular limits of quasilinear Hyperbolic Systems with large parameter and the incompressible limit of compressible Fluids. Comm. Pure Appl. Math. 24 (1981), pp. 481–524.ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    S. KALIRNEMAN et A. MAJDA: Formation of singularities for wave equations including the non linear vibrating string, Comm. Pure Appl. Math.Google Scholar
  20. [20]
    B. KEYFITZ et H. KRANZER: A system of non strictly Hyperbolic conservation law arising in Elasticity théory. Arch. for Rab. Mech. and Anal. 72 (1979).Google Scholar
  21. [21]
    S.N. KRUCKOV: First order quasilinear equations with several space variables, Math. USSR der Sbornik, 10 (1970), pp. 217–243.CrossRefGoogle Scholar
  22. [22]
    O.A. LADYZENSKAIA, SOLONNIKOV et URALTCEVA: Equations paraboliques linéaires et quasi-linéaires, Moscou (1967).Google Scholar
  23. [23]
    P.D. LAX: Hyperbolic Systems of Conservation Laws II, Comm. Pure Appl. Math. 10 (1957), pp. 537–566.MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    P.D. LAX: Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock waves, S.I.A.M. Regional conference Serie in Math. 11 (1973).Google Scholar
  25. [25]
    A.Y. LEROUX: A numerical Conception of Entropy for quasilinear equations Math. of Computation, 31, 140 (1977), pp. 848–872.MathSciNetCrossRefGoogle Scholar
  26. [26]
    A.Y. LEROUX: Numerical Stability for some equations of Gaz dynamic, Math. of Computation, 37, 156 (1981), pp. 307–320.ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    P.L. LIONS: Generalized solutions of Hamilton Jacobi equations Pitman, Londres research Lecture Notes, no69, Londres (1982).Google Scholar
  28. [28]
    T.P. LIU: The deterministic version of the Glimm Scheme, Comm. in Math. Physic, 57 (1977), pp. 135–148.ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    T.P. LIU: Uniqueness of weak solutions of the Cauchy problem for General 2 × 2 conservation Law. Jou. of Diff. Equations, 20, 2 (1976), pp. 369–388.ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    T.P. LIU et J. SMOLLER: The vacuum state in non isentropic gas dynamics Advances in Appl. Math. 1 (1980), pp. 345–359.MathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    J. MARSDEN: Well posedness of the equation of a non homogeneous perfect fluid, Comm. in Partial Diff. Equations, 1, 3 (1976), pp. 215–230.MathSciNetCrossRefGoogle Scholar
  32. [32]
    F. MURAT: L’injection du cône positif de H−1 dans W−1,q est compacte pour tout q > 2. (preprint).Google Scholar
  33. [33]
    F. MURAT: Compacité par Compensation Condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant, Ann.Scuola Norm. Sup. Pisa, 8 (1981), pp. 69–102.MathSciNetMATHGoogle Scholar
  34. [34]
    T. NISHIDA: Non linear hyperbolic equations and related topics in fluid dynamic, Publication Mathématiques d’Orsay, 78, 02. Université de Paris Sud, Dept. Mathématiques, Bat. 425, 91405, Orsay.Google Scholar
  35. [35]
    O. OLEINIK: On the uniqueness of the generalized solution of Cauchy problem for a non linear system of equations occuring in Mechanics, Uspeki Math. Nauk 73 (1957), pp. 165–176.Google Scholar
  36. [36]
    B. QUINN: Solutions with shocks an example if an L1 contraction semigroup. Comm. Pure Appl. Math. 24 (1971), pp. 125–132.MathSciNetCrossRefGoogle Scholar
  37. [37]
    J. SMOLLER: Shock waves and reaction diffusion equations, Springer (1983).Google Scholar
  38. [38]
    L. TARTAR: Compensated Compactness and application to partial differential equations in Research Notes on Mathematics, Non linear Analysis and Mechanics, Heriot Watt Symposium, Vol. 4, ed. R.J. KNOPS, Pitman Press (1979).Google Scholar
  39. [39]
    A.T. VOLPERT: The spaces B.V. and quasilinear equations-Math. USSR, Sb. 2 (1967), pp. 257–267.Google Scholar
  40. [40]
    L.C. YOUNG: Lectures on the Caculus of Variation and Optimal Control Theory, W.S. Saunders Philadelphia, Pa (1969).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • C. Bardos
    • 1
    • 2
  1. 1.Département de MathématiquesC.S.P. Université de Paris-NordVilletaneuseFrance
  2. 2.Centre de Mathématiques Appliquées Ecole Normale SupérieureParisFrance

Personalised recommendations