Sur le temps d'existence pour l'équation de Klein-Gordon semi-linéaire en dimension 1

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1. [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. Zbl0495.35024MR84h:35177
2. [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. Zbl0669.35073MR89e:35099
3. [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. Zbl0787.35097MR95d:35160a
4. [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. Zbl0861.35053MR97f:35018
5. [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. Zbl0741.35039MR92g:35140
6. [6] HÖRMANDER (L.). — Non-linear Hyperbolic Differential Equations, Lectures Notes in Lund, preprint, 1986-1987. 
7. [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. Zbl0787.35090MR94g:35196
8. [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. Zbl0848.35114MR96k:35159
9. [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. Zbl0597.35100MR87e:35080
10. [10] KLAINERMAN (S.) et MACHEDON (M.). — Smoothing estimates for null forms and applications, Duke Math. J., 1996, p. 99-131. Zbl0909.35094MR97h:35022
11. [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. Zbl0781.35062MR93k:35178
12. [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. Zbl0925.35139
13. [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. Zbl0877.35030MR97e:35112
14. [14] SHATAH (J.). — Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math., t. 38, 1985, p. 685-696. Zbl0597.35101MR87b:35160
15. [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. Zbl0783.35066MR94d:35110
16. [16] YORDANOV (B.). — Blow-up for the one-dimensional Klein-Gordon Equation with a cubic nonlinearity, preprint, 1996. 

1. Jean-Marc Delort, Temps d’existence pour l’équation de Klein-Gordon semi-linéaire à données petites faiblement décroissantes