Sur le temps d'existence pour l'équation de Klein-Gordon semi-linéaire en dimension 1
Bulletin de la Société Mathématique de France, Volume 125 (1997) no. 2, p. 269-311
@article{BSMF_1997__125_2_269_0,
     author = {Delort, Jean-Marc},
     title = {Sur le temps d'existence pour l'\'equation de Klein-Gordon semi-lin\'eaire en dimension 1},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {125},
     number = {2},
     year = {1997},
     pages = {269-311},
     doi = {10.24033/bsmf.2307},
     zbl = {0892.35102},
     mrnumber = {98i:35124},
     language = {fr},
     url = {http://www.numdam.org/item/BSMF_1997__125_2_269_0}
}
Delort, Jean-Marc. Sur le temps d'existence pour l'équation de Klein-Gordon semi-linéaire en dimension 1. Bulletin de la Société Mathématique de France, Volume 125 (1997) no. 2, pp. 269-311. doi : 10.24033/bsmf.2307. http://www.numdam.org/item/BSMF_1997__125_2_269_0/

[1] Bony (J.-M.). - Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles nonlinéaires, Ann. Sci. École Norm. Sup., t. 14, 1981, p. 209-256. | Numdam | MR 84h:35177 | Zbl 0495.35024

[2] Bony (J.-M.). - Second microlocalization and propagation of singularities for semilinear hyperbolic equations, Hyperbolic equations and related topics (Katata/Kyoto, 1984). - Academic Press, Boston, 1986, p. 11-49. | MR 89e:35099 | Zbl 0669.35073

[3] Bourgain (J.). - Fourier transforms restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, I, II, Geom. Funct. Anal., t. 3, 1993, p. 107-156, 202-262. | MR 95d:35160a | Zbl 0787.35097

[4] Fang (Y.-F.) et Grillakis (M.G.). - A priori estimates for the 2-d wave equation, Commun. Part. Diff. Eqs, t. 21, 1996, p. 1643-1665. | MR 97f:35018 | Zbl 0861.35053

[5] Georgiev (V.) et Popivanov (P.). - Global solutions to the two-dimensional Klein-Gordon equations, Commun. Part. Diff. Eqs, t. 16, 1991, p. 941-995. | MR 92g:35140 | Zbl 0741.35039

[6] Hörmander (L.). - Non-linear Hyperbolic Differential Equations, Lectures Notes in Lund, preprint, 1986-1987.

[7] Kenig (C.), Ponce (G.) et Vega (L.). - The Cauchy problem for the Korteweg-de-Vries equation on Sobolev spaces of negative indices, Duke Math. J., t. 71, 1993, p. 1-21. | MR 94g:35196 | Zbl 0787.35090

[8] Kenig (C.), Ponce (G.) et Vega (L.). - A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., t. 9, 1996, p. 573-603. | MR 96k:35159 | Zbl 0848.35114

[9] Klainerman (S.). - Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math., t. 38, 1985, p. 631-641. | MR 87e:35080 | Zbl 0597.35100

[10] Klainerman (S.) et Machedon (M.). - Smoothing estimates for null forms and applications, Duke Math. J., 1996, p. 99-131. | MR 97h:35022 | Zbl 0909.35094

[11] Kosecki (R.). - The Unit Condition and Global Existence for a Class of Nonlinear Klein-Gordon Equations, Jour. Diff. Eq., t. 100, 1992, p. 257-268. | MR 93k:35178 | Zbl 0781.35062

[12] Moriyama (K.), Tonegawa (S.) et Tsutsumi (Y.). - Almost Global Existence of Solutions for the Quadratic Semilinear Klein-Gordon Equation in One Space Dimension, preprint, 1996.

[13] Ozawa (T.), Tsutaya (K.) et Tsutsumi (Y.). - Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions, Math. Z., t. 222, 1996, p. 341-362. | MR 97e:35112 | Zbl 0877.35030

[14] Shatah (J.). - Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math., t. 38, 1985, p. 685-696. | MR 87b:35160 | Zbl 0597.35101

[15] Simon (J.C.H.) et Taflin (E.). - The Cauchy problem for nonlinear Klein-Gordon equations, Commun. Math. Phys., t. 152, 1993, p. 433-478. | MR 94d:35110 | Zbl 0783.35066

[16] Yordanov (B.). - Blow-up for the one-dimensional Klein-Gordon Equation with a cubic nonlinearity, preprint, 1996.