Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 34, Issue 1, 2001, Pages 1-61

  Delort, Jean Marc ^a  

^a University Sorbonne Paris Nord   (France)

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[No Author keywords available]

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EID: 0042238363     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(00)01059-4     Document Type: Article

References (23)

1. Alinhac S. Blow-up of small data solutions for a quasilinear wave equation in two space dimensions. Ann. of Math. (2). 149:(1):1997;97-127.
2. Alinhac S. Blow-up of small data solutions for a class of quasilinear wave equations in two space dimensions II. Acta Math. 182:(1):1999;1-23.
3. Bony J.-M. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4). 14:(2):1981;209-246.
4. Chemin J.-Y. Interaction contrôlée dans les équations aux dérivées partielles non linéaires. Bull. Soc. Math. France. 116:(3):1988;341-383.
5. Chemin J.-Y. Fluides parfaits incompressibles. Astérisque. 230:1995;. 177 p.
6. Christodoulou D. Global solutions of nonlinear hyperbolic equations for small initial data. Comm. Pure Appl. Math. 39:1986;267-282.
7. Delort J.-M. Minoration du temps d'existence pour l'équation de Klein-Gordon non linéaire en dimension 1 d'espace. Ann. Inst. Henri-Poincaré, Analyse non linéaire. 16:(5):1999;563-591.
8. Georgiev V., Yordanov B. Asymptotic behaviour of the one-dimensional Klein-Gordon equation with a cubic nonlinearity. Preprint. 1997.
9. Hörmander L. The lifespan of classical solutions of nonlinear hyperbolic equations. Lectures Notes in Math. 1256:1987;214-280 Springer-Verlag.
10. Hörmander L. Lectures on Nonlinear Hyperbolic Differential Equations. Mathématiques et Applications. 26:1997;Springer-Verlag.
11. Keel M., Tao T. Small data blow-up for semilinear Klein-Gordon equations. Amer. J. Math. 121:(3):1999;629-669.
12. Klainerman S. Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Comm. Pure Appl. Math. 38:1985;631-641.
13. Klainerman S. The null condition and global existence to nonlinear wave equations. Lectures in Applied Mathematics. 23:1986;293-326.
14. n+1 . Comm. Pure Appl. Math. 46:(2):1993;137-144.
15. Ladhari R. Petites solutions d'équations d'ondes quasi linéaires en dimension deux d'espace. Thèse. 1999;Université Paris-Sud.
16. Lindblad H., Sogge C. Restriction theorems and semilinear Klein-Gordon equations in (1+3) -dimensions. Duke Math. J. 85:(1):1996;227-252.
17. Moriyama K. Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one-space dimension. Differential Integral Equations. 10:(3):1997;499-520.
18. Moriyama K., Tonegawa S., Tsutsumi Y. Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension. Funkcialaj Ekvacioj. 40:(2):1997;313-333.
19. Ozawa T., Tsutaya K., Tsutsumi Y. 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.
20. Shatah J. Normal forms and quadratic nonlinear Klein-Gordon equations. Comm. Pure Appl. Math. 38:1985;685-696.
21. Simon J.C.H., Taflin E. The Cauchy problem for nonlinear Klein-Gordon equations. Comm. Math. Phys. 152:1993;433-478.
22. Yagi K. Normal forms and nonlinear Klein-Gordon equations in one space dimension. Master thesis. 1994;Waseda University.
23. Yordanov B. Blow-up for the one-dimensional Klein-Gordon equation with a cubic nonlinearity. Preprint. 1996.