Problèmes de Cauchy et ondes non linéaires
Journées équations aux dérivées partielles (1986), article no. 1, 29 p.
@article{JEDP_1986____A1_0,
     author = {M\'etivier, Guy},
     title = {Probl\`emes de {Cauchy} et ondes non lin\'eaires},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {1},
     publisher = {Ecole polytechnique},
     year = {1986},
     zbl = {0606.35051},
     mrnumber = {874543},
     language = {fr},
     url = {http://archive.numdam.org/item/JEDP_1986____A1_0/}
}
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Métivier, Guy. Problèmes de Cauchy et ondes non linéaires. Journées équations aux dérivées partielles (1986), article  no. 1, 29 p. http://archive.numdam.org/item/JEDP_1986____A1_0/

[1] S. Alinhac : Evolution d'une onde simple pour des équations non linéaires générales. | Numdam | Zbl

[2] S. Alinhac : Interaction d'ondes simples pour des équations complètement non linéaires. | Numdam | Zbl

[3] M. Beals - G. Metivier : Progressing wave solution to certain non linear mixed problem ; Duke Math. J. (to appear). | Zbl

[4] M. Beals - G. Metivier : Reflexion of transversal progressing waves in non linear strictly hyperbolic mixed problems ; Amer. J. Math (to appear). | Zbl

[5] J. Berning - M. Reed : Reflection of singularities of one dimensional semilinear wave equations at boundanes ; J. Math. Anal. Appl. 72 (1979) pp 635-653. | MR | Zbl

[6] J. M. Bony : Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires ; Ann. Sc. de l'Ecole Norm. Sup. 14 (1981) pp 209-246. | Numdam | MR | Zbl

[7] J. M. Bony : Interaction des singularités pour les équations aux dérivées partielles non linéaires ; Séminaire Goulaouic - Meyer - Schwartz, Ecole polytechnique ; Exposé n° 22 (1979-1980) et exposé n° 2 (1981-1982). | Numdam | Zbl

[8] J. M. Bony : Propagation et intéraction des singularités pour les solutions des équations aux dérivées partielles non linéaires ; Proc. Int. Conq. Math., Warszawa, (1983) pp 1133-1147. | MR | Zbl

[9] J. M. Bony : Interaction des singularités pour les équations de Klein - Gordon non linéaires ; Séminaire Goulaouic - Meyer - Schwartz, Ecole polytechnique ; exposé n° 10 (1983-1984). | Numdam | Zbl

[10] J. M. Bony : Second microlocalization and propagation of singularities for semilinear hyperbolic equations ; | Zbl

[11] J. Chazarain - A. Piriou : Introduction à la théorie des équations aux dérivées partielles ; Gauthier Villars, Paris (1981). | MR | Zbl

[12] R. Courant - K.O. Friedrichs : Supersonic Flow and Shock Waves ; Springer Verlag, New York 1949.

[13] R. Courant - D. Hilbert : Methods of Mathematical Physics, Wiley - Inter-science, New York 1962. | Zbl

[14] R. Di Perna : Uniquencess of solutions of hyperbolic conservation Paws ; Indiana V. Math. J. 28 (1979), pp 137-187. | MR | Zbl

[15] K. O. Friedrichs : Symmetric hyperbolic linear differential equations ; Comm. Pure Appl ; Math. 7 (1954) pp 345-392. | MR | Zbl

[16] J. Glimm : Solutions in the large for non linear hyperbolic systems of equations ; Comm. Pure Appl. Math. 18 (1965) pp 95-105. | MR | Zbl

[17] F. John : Formation of singularities in one dimensional non linear wave propagation ; Comm. Pure Appl Math, 27 (1974) pp 377-405. | MR | Zbl

[18] T. Kato : The Cauchy problem for quasilinear symmetric hyperbolic systems ; Arch. Rat. Mech. Anal. 58 (1975). | MR | Zbl

[19] H. O. Kreiss : Initial boundary value Problems for hyperbolic systems ; Comm. Pure Appl. Math, 23 (1970) pp 277-298. | MR | Zbl

[20] P. D. Lax : Hyperbolic systems of conservation laws II ; Comm. Pure Appl. Math, 10 (1957), pp 537-566. | MR | Zbl

[21] P. D. Lax : Schock waves and entropy ; Contributions to non linear functional Analysis ; (E. A. Zarantonello Ed) Academic Press, New York (1971).

[22] A. Majda : The stability of multidimensional schock fronts ; Mem. Amer Math. Soc, n° 275 (1983). | Zbl

[23] A. Majda : The existence of multidimensional schock fronts ; Mem. Amer Math. Soc, n° 281 (1983). | Zbl

[24] A. Majda : Compressible fluid flow and systems of conservation laws in several space variables ; Applied Math. Sc, 53, Springer verlag (1984). | MR | Zbl

[25] A. Majda - S. Osher : Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary ; Comm. Pure Appl. Math, 28 (1975) pp 607-676. | MR | Zbl

[26] A. Majda - R. Rosales : A theory for the spontaneous formation of Mach stems in reading shock fronts ; I the basic perturbation analysis ; SIAM J. Appl. Math (1984) pp 117-148. | MR | Zbl

[27] R. Melrose - N. Ritter : Interaction of non linear progressing waves for semilinear wave equations ; Ann Math, 121 (1985) pp 187-213. | MR | Zbl

[28] R. Melrose - N. Ritter : Interaction of non linear progressing waves for semilinear wave equations II ; | Zbl

[29] G. Metivier : Interaction de deux chocs pour un système de deux lois de conservation en dimension deux d'espace ; Trans. Amer. Math. Soc (à paraître). | Zbl

[30] G. Metivier : The Cauchy problem for semilinear hyperbolic systems with discontinuous data ; Dube Math. J. (à paraître). | Zbl

[31] G. Metivier : Propagation, interaction and reflection of discontinuous progressing waves for semilinear systems ; (preprint). | Zbl

[32] S. Mizohata : Lectures on the Cauchy problem ; Tata Inst., Bombay (1965). | MR | Zbl

[33] M. Oberguggenberger : Semilinear mixed hyperbolic systems in two variables : reflection and density of singularities (preprint).

[34] M. Oberguggenberger : Propagation and reflection of regularity of semilinear hyperbolic 2x2 systems in one space dimension ; (preprint). | Zbl

[35] O. A. Oleinik : Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation Usp. Mat. Nauk 14 (1959) pp 165-170, English Tranl in Amer. Math. Soc. Transl., ser 2 33 (1964) pp 285-290. | MR | Zbl

[36] J. Rauch : L2 is a continuable condition for Kreiss ' mixed problems ; Comm. Pure Appl. Math., 23 (1970) pp 221-232.

[37] J. Rauch : Symmetric positive systems with boundary Characteristic of constant multiplicity ; Trans. Amer. Math. Soc. 291 (1985) pp 167-187. | MR | Zbl

[38] J. Rauch - F. Massey : Differentiability of solutions to hyperbolic initial boundary value problems, Trans. Amer. Math. Soc, 189 (1974) pp 303-318. | MR | Zbl

[39] J. Rauch - M. Reed : Propagation of singularities for semilinear hyperbolic equations in one space variable, Ann of Math 111 (1980) pp 531-552. | MR | Zbl

[40] J. Rauch - M. Reed : Jump discontinuties of semilinear strictly hyperbolic systems in two variables : creation and propagation, Comm. Math. Phys, 81 (1981) pp 203-227. | MR | Zbl

[41] J. Rauch - M. Reed : Non linear microlocal analysis of semilinear hyperbolic systems in one space dimension, Duke Math. J. 49 (1982) pp 379-475. | MR | Zbl

[42] J. Rauch - M. Reed : Striated solutions to semilinear, two speed wave equations ; Indiana U ; Math. J, 34 1985 pp 337-353. | MR | Zbl

[43] J. Rauch - M. Reed : Discontinuous progressing waves for semilinear systems ; Comm. Partial Diff. Equ. 10 (1985). | MR | Zbl

[44] J. Rauch - M. Reed : Classical, conormal, semilinear waves, Seminaire Ecole Polytechnique, Exposé n° 5 (1985-1986). | Numdam | Zbl

[45] M. Ritter : Progressing wave solutions to non linear hyperbolic Cauchy problems ; Ph. D. thesis, M. I. T. (1984).

[46] J. Smoller : Shock waves and Reaction Diffusion Equations ; Springer Verlag, New York (1983). | MR | Zbl

[47] M. Taylor : Pseudodifferential operators ; Princeton University Press, Princeton (1981). | MR | Zbl

[48] M. Tougeron : Problème mixte avec condition de Neumann pour l'élastodynamique non linéaire (en préparation).