Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace

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1. [1] S. Alinhac, Blow-up for nonlinear hyperbolic equations, Progress in Nonlinear Differential Zbl0820.35001
2. Equations and their Applications, Birkäuser, Boston, 1995. 
3. [2] S. Alinhac, Explosion des solutions d'une équation d'onde quasi-linéaire en deux 
4. dimensions d'espace, Comm. Partial Diff. Eq.21 (5,6), (1996), 923-969. MR1391528
5. [3] S. Alinhac, Blow-up of small data solutions for a class of quasilinear wave equations in Zbl0896.35087
6. two space dimensions I, preprint, Université Paris-Sud, 1996. 
7. [4] S. Alinhac, Blow-up of small data solutions for a class of quasilinear wave equations in 
8. two space dimensions II, preprint, Université Paris-Sud, 1997. 
9. [5] D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math.39, (1986), 267-282. Zbl0612.35090MR820070
10. [6] R. Coifman et Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque57, 1978. Zbl0483.35082MR518170
11. [7] V. Georgiev, Decay estimates for the Klein-Gordon equations, Comm. Partial Diff. Eq.17, (1992), 1111-1139. Zbl0767.35068MR1179280
12. [8] V. Georgiev et B. Yordanov, Asymptotic behaviour of the one-dimensional Klein-Gordon 
13. equation with a cubic nonlinearity, preprint, 1997. 
14. [9] L. Hörmander, The lifespan of classical solutions of nonlinear hyperbolic equations, Springer Lectures Notes in Math.1256, (1987), 214-280. Zbl0632.35045MR897781
15. [10] L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications26, Springer, 1997. Zbl0881.35001MR1466700
16. [11] F. John, Blow-up of radial solutions of utt = c2 (ut)Δu in three space dimensions, Mat. Appl. Comput.4, (1985), 3-18. Zbl0597.35082MR808321
17. [12] F. John et S. Klainerman : Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math.37, (1984), 443-455. Zbl0599.35104MR745325
18. [13] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math.33, (1980), 43-101. Zbl0405.35056MR544044
19. [14] S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math38, (1985), 321-332. Zbl0635.35059MR784477
20. [15] S. Klainerman, The null condition and global existence to nonlinear wave equations, Lectures in Applied Mathematics23, (1986), 293-326. Zbl0599.35105MR837683
21. [16] S. Klainerman, Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math.38, (1985) 631-641. Zbl0597.35100MR803252
22. [17] K. Moriyama, Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one-space dimension, Diff. Int. Equations10, n° 3, (1997), 499-520. Zbl0891.35096MR1744859
23. [18] K. Moriyama, S. Tonegawa et Y. Tsutsumi, Almost Global Existence of Solutions for the Quadratic Semilinear Klein-Gordon Equation in One Space Dimension, Funkcialaj Ekvacioj40, n° 2, (1997) 313-333. Zbl0891.35142MR1480281
24. [19] T. Ozawa, K. Tsutaya et Y. Tsutsumi, Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions, Math. Z, 222, (1996) 341-362. Zbl0877.35030MR1400196
25. [20] J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math.38, (1985) 685-696. Zbl0597.35101MR803256
26. [21] J.C.H. Simon et E. Taflin, The Cauchy problem for nonlinear Klein-Gordon equations, Commun. Math. Phys.152, (1993) 433-478. Zbl0783.35066MR1213298
27. [22] K. Yagi, Normal forms and nonlinear Klein-Gordon equations in one space dimension, Master thesis, Waseda University, 1994. 
28. [23] B. Yordanov, Blow-up for the one-dimensional Klein-Gordon equation with a cubic nonlinearity, preprint, 1996. 

1. Jean-Marc Delort, Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1