Focusing and absorption of nonlinear oscillations
Journées équations aux dérivées partielles (1993), article no. 3, 11 p. 
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     author = {Joly, Jean-Luc and M\'etivier, Guy and Rauch, Jeff},
     title = {Focusing and absorption of nonlinear oscillations},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {3},
     pages = {1--11},
     year = {1993},
     publisher = {Ecole polytechnique},
     doi = {10.5802/jedp.442},
     zbl = {0815.35071},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/jedp.442/}
}
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Joly, Jean-Luc; Métivier, Guy; Rauch, Jeff. Focusing and absorption of nonlinear oscillations. Journées équations aux dérivées partielles (1993), article  no. 3, 11 p.. doi: 10.5802/jedp.442

[D] J.-M. Delort, Oscillations semi-linéaires multiphasées compatibles en dimension 2 et 3 d'espace, J.Diff.Eq. (1991). | Zbl

[DM] R. Diperna and A. Majda, The validity of geometric optics for weak solutions of conservation laws, Comm. Math. Phys. 98 (1985), 313-347. | MR | Zbl

[E] W. E, Propagation of oscillations in the solutions of 1-d compressible fluid equations, preprint.

[G1] O. Gues, Développments asymptoiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymptotic Anal. 1993. | Zbl

[G2] O. Gues Ondes multidimensionnelle epsilon stratifiées et oscillations, Duke Math. J., 1992. | MR | Zbl

[HK] J. Hunter and J. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), 547-569. | MR | Zbl

[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. | MR | Zbl

[JMR1] J.-L. Joly, G. Metivier, and J. Rauch, Resonant one dimensional nonlinear geometric optics, J. Funct. Anal., to appear. | Zbl

[JMR2] J. L. Joly, G. Metivier, and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Annals de l'Ecole Normale Superieur, to appear. | Numdam | Zbl

[JMR3] J. L. Joly, G. Metivier, and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., to appear. | Zbl

[JMR4] J.-L. Joly, G. Metivier, and J. Rauch, Focusing and absorbtion of nonlinear oscillations, preprint.

[J] J.L. Joly, Sur la propagation des oscillations semi-lineares en dimension 1 d'espace, C.R.Acad.Sc.Paris, t.296, 1983. | MR | Zbl

[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 | MR | Zbl

[JR2] J.L. Joly and J. Rauch, Justification of multidimensional single phase semilinear geometric optics, Trans. Amer. Math. Soc. 330 (1992), 599-625. | MR | Zbl

[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. | MR | Zbl

[MR] A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I : a single space variable, Stud. Appl. Math. 71 (1984), 149-179. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[S] S. Schochet, Fast singular limits of hyperbolic partial differential equations, J.Diff.Eq. to appear.

[Se] D. Serre, Oscillations non linéaires des systèmes hyperboliques : Méthodes et resultats qualitatifs, preprint. | Numdam | Zbl

[T] L. Tartar, Solutions oscillantes des équations de Carleman, Seminaire Goulaouic-Meyer-Schwartz, 1983. | Numdam

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