@article{ASENS_1995_4_28_1_51_0, author = {Joly, Jean-Luc and M\'etivier, Guy and Rauch, Jeffrey}, title = {Coherent and focusing multidimensional nonlinear geometric optics}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {28}, year = {1995}, pages = {51-113}, doi = {10.24033/asens.1709}, mrnumber = {95k:35035}, zbl = {0836.35087}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_1995_4_28_1_51_0} }
Joly, J.-L.; Métivier, G.; Rauch, J. Coherent and focusing multidimensional nonlinear geometric optics. Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995) pp. 51-113. doi : 10.24033/asens.1709. http://gdmltest.u-ga.fr/item/ASENS_1995_4_28_1_51_0/
[C] Oscillations de faible amplitude pour les systèmes 2 × 2 de lois de conservations, preprint Rennes, 1993. | Zbl 0852.35093
,[D] Oscillations semi-linéaires multiphasées compatibles en dimension 2 et 3 d'espace (Comm. in Partial Diff. Equ., Vol. 16, 1991, pp. 845-872). | MR 92g:35138 | Zbl 0736.35001
,[DPM] The validity of geometric optics for weak solutions (Comm. in Math. Phys., Vol. 98, 1985, pp. 313-347). | MR 87e:35057 | Zbl 0582.35081
and ,[G1] Développements asymptotiques de solutions exactes de systèmes hyperboliques quasi-linéaires (Asymptotic Analysis, Vol. 6, 1993, pp. 675-678). | MR 94b:35067 | Zbl 0780.35017
,[G2] Ondes multidimensionnelles ε-statifiées et oscillations (Duke Math. J., Vol. 68, 1992, pp. 401-446). | MR 94a:35011 | Zbl 0837.35086
,[HMR] Resonantly Interacting Weakly Nonlinear Hyperbolic Waves II : Several Space Variables (Stud. Appl. Math., Vol. 75, 1986, pp. 187-226). | MR 89h:35199 | Zbl 0657.35084
, and ,[JMR1] Resonant One Dimensional Nonlinear Geometric Optics (to appear in J. Funct. Analysis, Vol. 114, No. 1, 1993, pp. 106-231). | MR 94i:35118 | Zbl 0851.35023
, and ,[JMR2] Formal and Rigorous Nonlinear High Frequency Hyperbolic Waves, in Proceedings of Varenna Conference on Nonlinear Hyperbolic Equations and Field Theory, June 1990, M. K. MURPTY, S. SPAGNOLO eds. (Pitman Research Note in Math. Series, 1992, 121, p. 143). | Zbl 0824.35077
, and ,[JMR3] Remarques sur l'optique géométrique non linéaire multidimensionnelle, in Séminaire Équations aux dérivées partielles de l'École Polytechnique 1990-1991, Exposé n° 1. | Numdam | Zbl 0749.35055
, and ,[JMR4] Coherent Nonlinear Waves and the Wiener Algebra (Ann. Inst. Fourier, t. 44, 1994, pp. 167-196). | Numdam | MR 95c:35163 | Zbl 0791.35019
, and ,[JMR5] Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillary waves (to appear in Duke Math. J., Vol. 70, No. 2, 1993, pp. 373-404). | MR 94c:35048 | Zbl 0815.35066
, and ,[JMR6] Dense oscillations for the compressible 2-D Euler equations, in Non Linear Partial Differential Equations, Séminaire Collège de France 1992-1993, Pitmann Publ.
, and ,[JR1] Justification of Multidimensional Single Phase Semilinear Geometric Optics (Trans. Amer. Math. Soc., Vol. 330, 1992, pp. 599-625). | MR 92f:35040 | Zbl 0771.35010
and ,[JR2] Nonlinear Resonance can Create Dense Oscillations, in Microlocal Analysis and Nonlinear Waves, M. BEALS, R. MELROSE and J. B. RAUCH eds. (IMA Volumes in Math. and its Application, Vol. 30, Springer-Verlag). | MR 92k:35180 | Zbl 0794.35098
and ,[Ka1] Long Waves Asymptotics of Solutions of Nonlinear Systems of Equations with Dispersion (Dokl. An SSSR, Vol. 288, n° 4, 1986, and Soviet Math. Dokl., Vol. 33, n° 3, 1986, pp. 769-774). | MR 87j:35073 | Zbl 0629.35015
,[Ka2] Asymptotic Decay of a One Dimensional Wave Packet in a Nonlinear Dispersive Medium (Math. Sbornik Translation, Vol. 60, n° 2, 1988, pp. 457-484). | MR 88h:35069 | Zbl 0699.35135
,[Ka3] Long Waves Asymptotics. Integrable Equations as Asymptotic Limit of Nonlinear Systems (Russian Mth. Surveys, Vol. 44, n° 1, 1989, pp. 3-42). | MR 90g:58131 | Zbl 0683.35082
,[Ke] On solutions of nonlinear waves operators (Comm. Pure App. Math., Vol. 10, 1957, pp. 523-530). | MR 20 #3371 | Zbl 0090.31802
,[L1] Shock Waves and Entropy, in Contribution to Nonlinear Analysis, ZARANTONELLO ed., Academic Press, NY, 1971, pp. 603-634. | MR 52 #14677 | Zbl 0268.35014
,[L2] Asymptotic solutions of oscillatory initial value problems (Duke Math. J., Vol. 24, 1957, pp. 627-645). | MR 20 #4096 | Zbl 0083.31801
,[MR] Resonantly Interacting Weakly Nonlinear Hyperbolic Waves I : a Single Space Variables Stud. Appl. Math., Vol. 71, 1984, pp. 149-179). | MR 86e:35089 | Zbl 0572.76066
and ,[RR] Striated solutions of semilinear twospeed wave equations (Indiana Univ. Math. J., Vol. 34, 1985, pp. 337-353). | MR 86m:35111 | Zbl 0559.35053
and ,[S1] Fast singular limits of hyperbolic partial differential equations (to appear in J. Diff. Equ.). | Zbl 0838.35071
,[S2] Resonant nonlinear geometric optics for weak solutions of conservations laws, preprint 1992.
,[ST] Justification de l'optique géométrique faiblement non linéaire pour le problème mixte : cas des concentrations, preprint, 1993.
,