Minoration du temps d’existence pour l’équation de Klein-Gordon non-linéaire en dimension 1 d’espace
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 5, pp. 563-591.
@article{AIHPC_1999__16_5_563_0,
     author = {Delort, J.-M.},
     title = {Minoration du temps d{\textquoteright}existence pour l{\textquoteright}\'equation de {Klein-Gordon} non-lin\'eaire en dimension $1$ d{\textquoteright}espace},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {563--591},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     zbl = {0937.35160},
     mrnumber = {1712572},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPC_1999__16_5_563_0/}
}
TY  - JOUR
AU  - Delort, J.-M.
TI  - Minoration du temps d’existence pour l’équation de Klein-Gordon non-linéaire en dimension $1$ d’espace
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
DA  - 1999///
SP  - 563
EP  - 591
VL  - 16
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1999__16_5_563_0/
UR  - https://zbmath.org/?q=an%3A0937.35160
UR  - https://www.ams.org/mathscinet-getitem?mr=1712572
LA  - fr
ID  - AIHPC_1999__16_5_563_0
ER  - 
%0 Journal Article
%A Delort, J.-M.
%T Minoration du temps d’existence pour l’équation de Klein-Gordon non-linéaire en dimension $1$ d’espace
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 563-591
%V 16
%N 5
%I Gauthier-Villars
%G fr
%F AIHPC_1999__16_5_563_0
Delort, J.-M. Minoration du temps d’existence pour l’équation de Klein-Gordon non-linéaire en dimension $1$ d’espace. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 5, pp. 563-591. http://www.numdam.org/item/AIHPC_1999__16_5_563_0/

[1] S. Alinhac, Blow-up for nonlinear hyperbolic equations, Progress in Nonlinear Differential | Zbl

Equations and their Applications, Birkäuser, Boston, 1995.

[2] S. Alinhac, Explosion des solutions d'une équation d'onde quasi-linéaire en deux dimensions d'espace, Comm. Partial Diff. Eq. 21 (5,6), (1996), 923-969. | MR | Zbl

[3] S. Alinhac, Blow-up of small data solutions for a class of quasilinear wave equations in two space dimensions I, preprint, Université Paris-Sud, 1996.

[4] S. Alinhac, Blow-up of small data solutions for a class of quasilinear wave equations in two space dimensions II, preprint, Université Paris-Sud, 1997. | Zbl

[5] D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39, (1986), 267-282. | MR | Zbl

[6] R. Coifman et Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57, 1978. | MR | Zbl

[7] V. Georgiev, Decay estimates for the Klein-Gordon equations, Comm. Partial Diff. Eq. 17, (1992), 1111-1139. | MR | Zbl

[8] V. Georgiev et B. Yordanov, Asymptotic behaviour of the one-dimensional Klein-Gordon

equation with a cubic nonlinearity, preprint, 1997.

[9] L. Hörmander, The lifespan of classical solutions of nonlinear hyperbolic equations, Springer Lectures Notes in Math. 1256, (1987), 214-280. | MR | Zbl

[10] L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications 26, Springer, 1997. | MR | Zbl

[11] F. John, Blow-up of radial solutions of utt = c2 (ut)Δu in three space dimensions, Mat. Appl. Comput. 4, (1985), 3-18. | MR | Zbl

[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. | MR | Zbl

[13] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33, (1980), 43-101. | MR | Zbl

[14] S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math 38, (1985), 321-332. | MR | Zbl

[15] S. Klainerman, The null condition and global existence to nonlinear wave equations, Lectures in Applied Mathematics 23, (1986), 293-326. | MR | Zbl

[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. | MR | Zbl

[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. Equations 10, n° 3, (1997), 499-520. | MR | Zbl

[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 Ekvacioj 40, n° 2, (1997) 313-333. | MR | Zbl

[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. | EuDML | MR | Zbl

[20] J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math. 38, (1985) 685-696. | MR | Zbl

[21] J.C.H. Simon et E. Taflin, The Cauchy problem for nonlinear Klein-Gordon equations, Commun. Math. Phys. 152, (1993) 433-478. | MR | Zbl

[22] K. Yagi, Normal forms and nonlinear Klein-Gordon equations in one space dimension, Master thesis, Waseda University, 1994.

[23] B. Yordanov, Blow-up for the one-dimensional Klein-Gordon equation with a cubic nonlinearity, preprint, 1996.