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Etude des oscilaltions dans les equations aux derivees partielles non lineaires

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Bibliographie pour la partie I /1/Bensoussan A.-Lions J.L.-Papanicolaou G.: Asymptotic analysis for periodic structures. Studies in mathematics and its applications 5 North-Holland.

  1. Bergman D.: The dielectric constant of a composite material a problem in classical physics, Phys. Rep C 43, 1978, p. 377–407.

    Article  ADS  MathSciNet  Google Scholar 

  2. Bergman D.: Resonances in the bulk properties of composite media-theory and applications p. 10–37, Macroscopic properties of disordered media, Lecture Notes in Physics 154, Springer-Verlag.

    Google Scholar 

  3. Cioranescu D.-Murat F.: Un terme étrange venu d'ailleurs I, II, p. 98–138, p. 154–178 Non linear partial differential equations and their applications. Collège de France Seminar Vol. II, III. Research Notes in Mathematics 60, 70. Pitman.

    Google Scholar 

  4. Joseph D.-Renardy M.-Renardy Y.: Instability of the flow of immiscible liquids with different viscosities in a pipe. MRC report 2503, à paraître.

    Google Scholar 

  5. Kohler W.-Papanicolaou G.: Bounds for the effective conductivity of random media p. III-130, Macroscopic properties of disordered media, Lecture Notes in Physics 154, Springer-Verlag.

    Google Scholar 

  6. Lurie K.A.-Cherkaev A.V.-Sedorov A.V.: Regularization of optimal design problems for bars and plates. Journal of optimization theory and applications vol. 37, 1982, p. 499–543.

    Article  MATH  MathSciNet  Google Scholar 

  7. Milton G.-McPhedran R.C.: A comparison of two methods for deriving bounds on the effective conductivity of composites p. 183-193, Macroscopic properties of disordered media, Lecture Notes in Physics 154, Springer-Verlag.

    Google Scholar 

  8. Murat F.: Compacité par compensation. Ann. Sc. Norm. Sup. Pisa 5, 3. 1978 p. 489–507.

    MATH  Google Scholar 

  9. Murat F.: Compacité par compensation II p. 245–256. Proceedings of the international meeting on recent methods in non linear analysis (Rome, Mai 1978). Pitagora Editrice. Bologna (1979).

    Google Scholar 

  10. Murat F.: Compacité par compensation III. Ann. Sc. Norm. Sup. Pisa 8.1981, p. 69–102.

    MATH  Google Scholar 

  11. Sanchez-Palencia E.: Non homogeneous media and vibration theory, Lecture Notes in Physics 127, Springer-Verlag.

    Google Scholar 

  12. Serrin J.: A symmetry problem in potential theory. Arch. Rat. Mech. Anal. Vol. 43, 4. 1971 p. 304–318.

    Article  MATH  MathSciNet  Google Scholar 

  13. Weinberger H.: Remark on the preceding paper of Serrin. Arch. Rat. Mech. Anal. Vol. 43, 4. 1971 p. 319–320.

    Article  MATH  MathSciNet  Google Scholar 

Pour les détails manquants dans cet exposé (en attendant une rédaction plus complete) on pourra se reporter a mes publications antérieures

  1. Compensated compactness and applications to partial differential equations p. 136-212, Non linear analysis and mechanics Heriot-Watt symposium Vol. IV. Research Notes in mathematics 39, Pitman.

    Google Scholar 

  2. Quelques remarques sur l'homogénéisation p. 469-481. Japan-France Seminar Tokyo and Kyoto 1976, H. Fujita ed. Japan Society for the promotion of Science 1978.

    Google Scholar 

  3. Homogénéisation en hydrodynamique p. 474-481. Singular perturbations and boundary layer theory. Lecture Notes in mathematics 594 Springer-Verlag.

    Google Scholar 

  4. Estimation de coefficients homogénéisés p. 364–373. Computing methods in applied sciences and engineering 1977. I. Lecture Notes in Mathematics vol. 704. Springer-Verlag.

    Google Scholar 

  5. Problèmes de contrôle de coefficients dans des équations aux dérivées partielles, p. 420–426. Control theory, numerical methods and computer systems modelling, Lecture Notes in Economics and:Mathematical Systems 107, Springer-Verlag.

    Google Scholar 

Bibliographie pour la partie II

  1. Cabannes H.: Solution globale d'un probleme de Cauchy en théorie cinétique discrète, modèle plan. C.R. Acad. Sci. Paris t.284 (1977) p. 269–272.

    MATH  Google Scholar 

  2. Cabannes H.: Solution globale d'un problème de Cauchy en théorie cinétique discrète, modèle spatial. C.R. Acad. Sci. Paris t.284 (1977) p. 347–350.

    MATH  Google Scholar 

  3. Di Perna R.: Convergence of approximate solutions to conservation laxs. Arch. Rat. Mech. Anal. 82 n° 1, 1983, p. 27–70.

    Google Scholar 

  4. Hamdache K.: Existence globale et comportement asymptotique pour l'équation de Boltzmann à répartition discrète de vitesse. C.R. Acad. Sci. Paris (1983) à paraitre.

    Google Scholar 

  5. Illner R.: Global existence results for discrete velocity models of the Boltzmann equation in several dimensions. Jour. Meca. Th. Appl. Vol. 1, 4, (1982) p. 611–622.

    MATH  MathSciNet  Google Scholar 

  6. Illner R.-Reed, M.: Decay of solutions of the Carleman model, Math. Meth. Appl. Sci. 3 (1981) p. 121–127.

    Article  MATH  MathSciNet  Google Scholar 

  7. Kawashima S.: Global solution of the initial value problem for a discrete velocity model of the Boltzmann equation, Proc. Japan. Acad. 57 (1981) p. 19–24.

    Article  MATH  MathSciNet  Google Scholar 

  8. Mimura M.-Nishida T.: On the Broad well's model for a simple discrete velocity gas. Proc. Japan. Acad. 50 (1974) p. 812–817.

    Article  MATH  MathSciNet  Google Scholar 

En attendant une rédaction plus complète on trouvera certains des détails manquants ici dans mes publications antérieures

  1. Existence globale pour un système hyperbolique semi linéaire de la théorie cinétique des gaz. Séminaire Goulaouic Schwartz 1975–1976. I

    Google Scholar 

  2. Some existence theorems for semi linear hyperbolic systems in one space variable. MRC report ≠ 2164. University of Wiscoussis, Madison.

    Google Scholar 

  3. Solutions oscillantes des équations de Carleman Séminaire Goulaouic-Meyer-Schwartz 1980–1981 n° XII.

    Google Scholar 

Pour l'application de ces idées aux systèmes hyperboliques quasilinéaires que je-n'ai pas abordées ici

  1. The compensated compactness method applied to systems of conservation laws, p. 263–285, systems of nonlinear partial differential equations, ed. J.P4. Ball, Nato ASI series C111, Reidel.

    Google Scholar 

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  1. Ecole Polytechnique et C.E.A. B.P. n° 27, 94190, Villeneuve St Georges, France

    L. Tartar

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  1. L. Tartar
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Philippe G. Ciarlet Maurice Roseau

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© 1984 Springer-Verlag

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Tartar, L. (1984). Etude des oscilaltions dans les equations aux derivees partielles non lineaires. In: Ciarlet, P.G., Roseau, M. (eds) Trends and Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12916-2_68

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  • DOI: https://doi.org/10.1007/3-540-12916-2_68

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