@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}, mrnumber = {1712572}, zbl = {0937.35160}, language = {fr}, url = {http://archive.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 SP - 563 EP - 591 VL - 16 IS - 5 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1999__16_5_563_0/ 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 %U http://archive.numdam.org/item/AIHPC_1999__16_5_563_0/ %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://archive.numdam.org/item/AIHPC_1999__16_5_563_0/
[1] Blow-up for nonlinear hyperbolic equations, Progress in Nonlinear Differential | Zbl
,Equations and their Applications, Birkäuser, Boston, 1995.
[2] 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] Blow-up of small data solutions for a class of quasilinear wave equations in two space dimensions I, preprint, Université Paris-Sud, 1996.
,[4] 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] Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39, (1986), 267-282. | MR | Zbl
,[6] Au-delà des opérateurs pseudo-différentiels, Astérisque 57, 1978. | Numdam | MR | Zbl
et ,[7] Decay estimates for the Klein-Gordon equations, Comm. Partial Diff. Eq. 17, (1992), 1111-1139. | MR | Zbl
,[8] Asymptotic behaviour of the one-dimensional Klein-Gordon
et ,equation with a cubic nonlinearity, preprint, 1997.
[9] The lifespan of classical solutions of nonlinear hyperbolic equations, Springer Lectures Notes in Math. 1256, (1987), 214-280. | MR | Zbl
,[10] Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications 26, Springer, 1997. | MR | Zbl
,[11] Blow-up of radial solutions of utt = c2 (ut)Δu in three space dimensions, Mat. Appl. Comput. 4, (1985), 3-18. | MR | Zbl
,[12] Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37, (1984), 443-455. | MR | Zbl
et :[13] Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33, (1980), 43-101. | MR | Zbl
,[14] Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math 38, (1985), 321-332. | MR | Zbl
,[15] The null condition and global existence to nonlinear wave equations, Lectures in Applied Mathematics 23, (1986), 293-326. | MR | Zbl
,[16] 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] 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] 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
, et ,[19] 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
, et ,[20] Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math. 38, (1985) 685-696. | MR | Zbl
,[21] The Cauchy problem for nonlinear Klein-Gordon equations, Commun. Math. Phys. 152, (1993) 433-478. | MR | Zbl
et ,[22] Normal forms and nonlinear Klein-Gordon equations in one space dimension, Master thesis, Waseda University, 1994.
,[23] Blow-up for the one-dimensional Klein-Gordon equation with a cubic nonlinearity, preprint, 1996.
,