@article{JEDP_1990____A7_0, author = {Joly, Jean-Luc and M\'etivier, Guy and Rauch, Jeff}, title = {Rigorous resonant 1-d nonlinear geometric optics}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {7}, pages = {1--12}, publisher = {Ecole polytechnique}, year = {1990}, mrnumber = {92e:35104}, zbl = {0718.35094}, language = {en}, url = {http://www.numdam.org/item/JEDP_1990____A7_0/} }
TY - JOUR AU - Joly, Jean-Luc AU - Métivier, Guy AU - Rauch, Jeff TI - Rigorous resonant 1-d nonlinear geometric optics JO - Journées équations aux dérivées partielles PY - 1990 SP - 1 EP - 12 PB - Ecole polytechnique UR - http://www.numdam.org/item/JEDP_1990____A7_0/ LA - en ID - JEDP_1990____A7_0 ER -
Joly, Jean-Luc; Métivier, Guy; Rauch, Jeff. Rigorous resonant 1-d nonlinear geometric optics. Journées équations aux dérivées partielles (1990), article no. 7, 12 p. http://www.numdam.org/item/JEDP_1990____A7_0/
[CB] Ondes asymptotiques et approchées pour systèmes d'equations aux dérivées partielles nonlineares, J. Math. Pure Appl. 48 (1969), 117-158. | MR | Zbl
,[DM] The validity of geometric optics for weak solutions of conservation laws, Comm. Math. Phys. 98 (1985), 313-347. | MR | Zbl
and ,[G] These Rennes, January 1989, and article to appear.
,[H] Homogenization for semilinear hyperbolic systems with oscillatory data, Comm. Pure Appl. Math 41 (1988) 471-495. | MR | Zbl
,[HK] Weakly nonlinear high frequency waves, Comm. Pure Appl. Math. 36 (1983), 547-569. | MR | Zbl
and ,[HMR] Resonantly interacting weakly nonlinear hyperbolic waves II : several space variables, Stud. Appl. Math. 75 (1986), 187-226. | MR | Zbl
, , and, ,[J] Sur la propagations des oscillations semi-lineares en dimension 1 d'espace, C.R. Acad. Sc. Paris, t. 296, 1983. | MR | Zbl
,[JMR1] Formal and rigorous nonlinear high frequency waves, in Proceedings of Conference on Nonlinear Hyperbolic Equations, Como 1990, Pittman Publ.
, , and ,[JMR2] One dimensional nonlinear geometric optics, preprint. | Zbl
, , and ,[JR1] Ondes oscillantes semi-linéaires en 1.d, Journées Equations aux Dérivées Partielles, St. Jean de Monts, Juin 1986, Publ. de l'École Polytechnique, Palaiseau. | Numdam | MR | Zbl
and ,[JR2] Ondes oscillantes semi-linéaire à hautes fréquences, in Recent Developments in Hyperbolic Equations, (L. Cattabriga, F. Colombini, M. Murthy, S. Spagnolo, eds.), Pitman Research Notes in Math., 183 (1988), 103-115. | MR | Zbl
and ,[JR3] High frequency semilinear oscillations, in Wave Motion : Theory, Modeling, and Computation (A. J. Chorin and A. J. Majda, eds.), Springer-Verlag, (1987) 202-217. | MR | Zbl
and ,[JR4] Nonlinear resonance can create dense oscillations, in Microlocal Analysis and Nonlinear Waves, M. Beals, R. Melrose, and J. Rauch eds., Springer-Verlag to appear. | Zbl
and ,[JR5] Justification of multidimensional single phase semilinear geometric optics, preprint. | Zbl
and ,[MR] Resonantly interacting weakly nonlinear hyperbolic waves I : a single space variable, Stud. Appl. Math. 71 (1984), 149-179. | MR | Zbl
and ,[MRS] A canonical system of integro differential equations in nonlinear acoustics, Stud. Appl. Math. 79 (1988), 205-262. | MR | Zbl
, , and, ,[MPT] Weak limits of semilinear Hyperbolic systems with oscillating data, Lecture Notes in Physics 230, Springer-Verlag 1985, 277-289. | MR | Zbl
, , ,[P] Some explicit resonating waves in weakly nonlinear gas dynamics, Studies in Applied Math 79 (1988), 263-270. | MR | Zbl
,[T] Solutions oscillantes des equations de Carleman, Seminaire Goulaouic-Meyer-Schwartz, 1983. | Numdam
,