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The interaction of two progressing waves

  • Guy Métivier
  • Jeffrey Rauch
Hyperbolic P.D.E. Theory
  • 334 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1402)

Keywords

Hyperbolic System Light Cone Piecewise Smooth Incoming Wave Logarithmic Singularity 
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. [A]
    S. Alinhac, Evolution d'une onde simple pour les équations non-linéaires génerales, preprint.Google Scholar
  2. [Be]
    M. Beals, Presence and absence of weak singularities in nonlinear waves, in Dynamical Problems in Continuum Physics, eds. Bona, Dafermos, Erikson, and Kinderlehrer, Springer-Verlag, New York, 1987, p. 23–41.CrossRefGoogle Scholar
  3. [Bo1]
    J-M. Bony, Interaction des singularités pour les équations aux déerivées partielles non-linéaires, Séminaire Goulaouic-Meyer-Schwartz, 1981–82, exposé #2.Google Scholar
  4. [Bo2]
    J-M. Bony, Propagation et interaction des singularités par les solutions des équations aux dérivées partielles non linéaires, Proc. Int. Cong. Math., Warsaw (1983), 1133–1147Google Scholar
  5. [C]
    R. Courant, Methods of Mathematical Physics, vol.II, Interscience, New York, 1966.Google Scholar
  6. [CL]
    R. Courant and P.D. Lax, The propagation of discontinuities in wave motion, Proc. Natl. Acad. Sci. USA 42(1956), p. 872–876.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [Ha]
    J. Hadamard, Lecons sur la Propagation des Ondes et les Equations de l'Hydrodynamique, A. Hermann, Paris, 1903.zbMATHGoogle Scholar
  8. [Ho]
    L. Hormander, The Analysis of Linear Partial Differential Operators, vol. III, Springer-Verlag, New York, 1985.zbMATHGoogle Scholar
  9. [Mel]
    R. Melrose, Interaction of progressing waves through a nonlinear potential, Séminaire Goulaouic-Meyer-Schwartz, 1983/84, expose #12.Google Scholar
  10. [M]
    G. Metivier, The Cauchy problem for semilinear hyperbolic systems with discontinuous data, Duke Math. J. 53(1986), p. 983–1011.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [MR]
    G. Metivier and J. Rauch, article in preparation.Google Scholar
  12. [NP1]
    B. Nadir and A. Piriou, Symboles pour deux ondes conormales sans interaction, C.R.A.S. Paris, t.305, serie 1 (1987).Google Scholar
  13. [NP2]
    B. Nadir and A. Piriou, Ondes semi-linéare conormales par rapport á deux hypersurfaces transverses, to appear.Google Scholar
  14. [P1]
    A. Piriou, Calcul symbolique nonlinéare pour une onde conormale simple, C.R.A.S. Paris t.304, serie 1, #4(1987).Google Scholar
  15. [P2]
    A. Piriou, private communication.Google Scholar
  16. [P3]
    A. Piriou, article to appear in Ann. Inst. Fourier.Google Scholar
  17. [RR1]
    J. Rauch and M. Reed, Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: creation and propagation, Comm. Math. Phys. 81(1981) p. 203–227.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [RR2]
    J. Rauch and M. Reed, Discontinuous progressing waves for semilinear systems, Comm. P.D.E. 10(1985), p. 1033–1075.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [RR3]
    J. Rauch and M. Reed, Striated solutions of semilinear two-speed wave equations, Indiana Math. J. 34(1985) p. 337–353.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [RR4]
    J. Rauch and M. Reed, Classical Conormal Solutions of Semilinear Systems, Comm. P.D.E. 13(1988) p. 1297–1335.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [RR5]
    J. Rauch and M.Reed, Bounded stratified and striated solutions of hyperbolic systems, in Nonlinear Partial Differential Equations and thier Applications, Séminaire Collège de France 1987, H. Brezis and J.L. Lions eds.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Guy Métivier
    • 1
  • Jeffrey Rauch
    • 2
  1. 1.IRMAR Universite de Rennes I, Campus BeaulieuRennes CedexFrance
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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