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Introduction Aux Problemes Hyperboliques Non Lineaires

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Bibliographie

  1. P. COLELLA, GLIMM: Methods for Gaz Dynamic, SIAM Journal on Scientific an-Statistical Compating, Vol 3, pp. 76–110 (1982).

    CrossRef  Google Scholar 

  2. J. CONLON and T.P. LIU: Admissibility criteria for hyperbolic conservation Law. Indiana Univ. Math. J 30 (1981) 5, pp. 641–652.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. A.J. CHORIN: Random Choice Solution of Hyperbolic System. Journ. of Comp. Phys. 22, 2 (1976), pp. 517–533.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  5. A.J. CHORIN: Random Choice Methods with applications to Reaction Gas Flow, Journ. of Comp. Phys. 25, 3 (1977), pp. 253–272.

    CrossRef  ADS  MATH  Google Scholar 

  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.

    CrossRef  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. C. DAFERMOS: The entropy rate admissibility criteria for solutions of hyperbolic conservation Laws. Journ. of Diff. Equations, 14, 2 (1973), pp. 202–212.

    CrossRef  ADS  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  10. R. Di PERNA: Uniqueness of Solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 28 (1979), pp. 137–187.

    CrossRef  MathSciNet  Google Scholar 

  11. R. Di PERNA: à paraître aux Archiv for Mech. and Analysis (1983).

    Google Scholar 

  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.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  13. J. GLIMM: Solution in the large for non linear hyperbolic systèmes of equations. Comm. Pure Apl. Math. 18 (1965), pp. 697–715.

    CrossRef  MATH  Google Scholar 

  14. GOLUBITZKY et D. SCHAEFFER: Stability of schock waves for a single conservation law. Advances in Math. 16 (1975) pp. 65–71.

    CrossRef  MathSciNet  Google Scholar 

  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.

    CrossRef  Google Scholar 

  16. E. HOPF: The partial differential equation ut+uux=uxx, Comm. Pure App. Math. 3 (1950), pp. 201–230.

    CrossRef  Google Scholar 

  17. T. KATO: The Cauchy Problem for quasilinear Symmetric Hyperbolic Systems Ard. Pub. Mech. and Anal., 58, 3 (1975), pp. 181–205.

    MATH  Google Scholar 

  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.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  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. 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. S.N. KRUCKOV: First order quasilinear equations with several space variables, Math. USSR der Sbornik, 10 (1970), pp. 217–243.

    CrossRef  Google Scholar 

  22. O.A. LADYZENSKAIA, SOLONNIKOV et URALTCEVA: Equations paraboliques linéaires et quasi-linéaires, Moscou (1967).

    Google Scholar 

  23. P.D. LAX: Hyperbolic Systems of Conservation Laws II, Comm. Pure Appl. Math. 10 (1957), pp. 537–566.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. A.Y. LEROUX: A numerical Conception of Entropy for quasilinear equations Math. of Computation, 31, 140 (1977), pp. 848–872.

    CrossRef  MathSciNet  Google Scholar 

  26. A.Y. LEROUX: Numerical Stability for some equations of Gaz dynamic, Math. of Computation, 37, 156 (1981), pp. 307–320.

    CrossRef  ADS  MathSciNet  Google Scholar 

  27. P.L. LIONS: Generalized solutions of Hamilton Jacobi equations Pitman, Londres research Lecture Notes, no69, Londres (1982).

    Google Scholar 

  28. T.P. LIU: The deterministic version of the Glimm Scheme, Comm. in Math. Physic, 57 (1977), pp. 135–148.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  30. T.P. LIU et J. SMOLLER: The vacuum state in non isentropic gas dynamics Advances in Appl. Math. 1 (1980), pp. 345–359.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  Google Scholar 

  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. 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.

    MathSciNet  MATH  Google Scholar 

  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. 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. B. QUINN: Solutions with shocks an example if an L1 contraction semigroup. Comm. Pure Appl. Math. 24 (1971), pp. 125–132.

    CrossRef  MathSciNet  Google Scholar 

  37. J. SMOLLER: Shock waves and reaction diffusion equations, Springer (1983).

    Google Scholar 

  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. A.T. VOLPERT: The spaces B.V. and quasilinear equations-Math. USSR, Sb. 2 (1967), pp. 257–267.

    Google Scholar 

  40. L.C. YOUNG: Lectures on the Caculus of Variation and Optimal Control Theory, W.S. Saunders Philadelphia, Pa (1969).

    Google Scholar 

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Bardos, C. (1984). Introduction Aux Problemes Hyperboliques Non Lineaires. In: Beirão da Veiga, H. (eds) Fluid Dynamics. Lecture Notes in Mathematics, vol 1047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072326

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  • DOI: https://doi.org/10.1007/BFb0072326

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