Focusing and absorption of nonlinear oscillations

Jean-Luc Joly; Guy Métivier; Jeff Rauch

Journées équations aux dérivées partielles (1993)

  • Volume: 1993, Issue: 3, page 1-11
  • ISSN: 0752-0360

How to cite

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Joly, Jean-Luc, Métivier, Guy, and Rauch, Jeff. "Focusing and absorption of nonlinear oscillations." Journées équations aux dérivées partielles 1993.3 (1993): 1-11. <http://eudml.org/doc/93272>.

@article{Joly1993,
author = {Joly, Jean-Luc, Métivier, Guy, Rauch, Jeff},
journal = {Journées équations aux dérivées partielles},
keywords = {fast oscillating initial functions; passage of the fast oscillating wave through a focal point},
language = {eng},
number = {3},
pages = {1-11},
publisher = {Ecole polytechnique},
title = {Focusing and absorption of nonlinear oscillations},
url = {http://eudml.org/doc/93272},
volume = {1993},
year = {1993},
}

TY - JOUR
AU - Joly, Jean-Luc
AU - Métivier, Guy
AU - Rauch, Jeff
TI - Focusing and absorption of nonlinear oscillations
JO - Journées équations aux dérivées partielles
PY - 1993
PB - Ecole polytechnique
VL - 1993
IS - 3
SP - 1
EP - 11
LA - eng
KW - fast oscillating initial functions; passage of the fast oscillating wave through a focal point
UR - http://eudml.org/doc/93272
ER -

References

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  2. [DM] R. Diperna and A. Majda, The validity of geometric optics for weak solutions of conservation laws, Comm. Math. Phys. 98 (1985), 313-347. Zbl0582.35081MR87e:35057
  3. [E] W. E, Propagation of oscillations in the solutions of 1-d compressible fluid equations, preprint. 
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  5. [G2] O. GuesOndes multidimensionnelle epsilon stratifiées et oscillations, Duke Math. J., 1992. Zbl0837.35086MR94a:35011
  6. [HK] J. Hunter and J. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), 547-569. Zbl0547.35070MR85h:35143
  7. [HMR] J. Hunter, A. Majda, and, R. Rosales, Resonantly ineteracting weakly nonlinear hyperbolic waves II : several space variables, Stud. Appl. Math. 75 (1986), 187-226. Zbl0657.35084MR89h:35199
  8. [JMR1] J.-L. Joly, G. Metivier, and J. Rauch, Resonant one dimensional nonlinear geometric optics, J. Funct. Anal., to appear. Zbl0851.35023
  9. [JMR2] J. L. Joly, G. Metivier, and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Annals de l'Ecole Normale Superieur, to appear. Zbl0836.35087
  10. [JMR3] J. L. Joly, G. Metivier, and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., to appear. Zbl0815.35066
  11. [JMR4] J.-L. Joly, G. Metivier, and J. Rauch, Focusing and absorbtion of nonlinear oscillations, preprint. Zbl0815.35071
  12. [J] J.L. Joly, Sur la propagation des oscillations semi-lineares en dimension 1 d'espace, C.R.Acad.Sc.Paris, t.296, 1983. Zbl0555.35081MR84j:35112
  13. [JR1] J.L. Joly and J. Rauch, Nonlinear resonance can create dense oscillations, in Microlocal Analysis and Nonlinear Waves, M. Beals, R. Melrose, and J. Rauch eds., Springer-Verlag (1991) 113-123 Zbl0794.35098MR92k:35180
  14. [JR2] J.L. Joly and J. Rauch, Justification of multidimensional single phase semilinear geometric optics, Trans. Amer. Math. Soc. 330 (1992), 599-625. Zbl0771.35010MR92f:35040
  15. [Kal] L.A. Kalyakin, Long wave asymptotics, integrable equations as asymptotic limit of nonlinear systems, Russian Math Surveys vol.44 no.1 (1989), 3-42. Zbl0683.35082MR90g:58131
  16. [MR] A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I : a single space variable, Stud. Appl. Math. 71 (1984), 149-179. Zbl0572.76066MR86e:35089
  17. [MRS] A. Majda, R. Rosales, and M. Schonbek, A canonical system of integro-differential equations in nonlinear acoustics, Stud. Appl. Math. 79 (1988), 205-262. Zbl0669.76103MR90g:76077
  18. [MPT] D. MacLaughlin, G. Papanicolau, L. Tartar, Weak limits of semilinear Hyperbolic systems with oscillating data, Lecture Notes in Physics 230, Springer-Verlag 1985, 277-289. Zbl0588.76137MR815948
  19. [S] S. Schochet, Fast singular limits of hyperbolic partial differential equations, J.Diff.Eq. to appear. Zbl0838.35071
  20. [Se] D. Serre, Oscillations non linéaires des systèmes hyperboliques : Méthodes et resultats qualitatifs, preprint. Zbl0810.35060
  21. [T] L. Tartar, Solutions oscillantes des équations de Carleman, Seminaire Goulaouic-Meyer-Schwartz, 1983. Zbl0481.35010

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