A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension

Kyoto Journal of Mathematics

Volumn 39, Issue 2, 1999, Pages 203-213

  Katayama, Soichiro ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033476185     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250517908     Document Type: Article

References (19)

1. D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math., 39 (1986), 267-282.
2. V. Georgiev, Global solution of the system of wave and Klein-Gordon equations, Math Z., 203 (1990), 683-698.
3. V. Georgiev, Decay estimates for the Klein-Gordon equation, Commun. in Partial Differential Equations, 17 (1992), 1111-1139.
4. V. Georgiev and P. Popivanov, Global solution to the two dimensional Klein-Gordon equation, Commun. in Partial Differential Equations, 16 (1991), 941-995.
5. L. Hörmander, Remarks on the Klein-Gordon equation, Journées "Equations aux dérivées partielles", Saint-Jean-Monts, Conférence no. 1, Soc. Math. France, 1987.
6. S. Katayama, Global existence for systems of nonlinear wave equations in two space dimensions, Publ. RIMS, Kyoto Univ., 29 (1993), 1021-1041.
7. S. Katayama, Global existence for systems of nonlinear wave equations in two space dimensions, II, Publ. RIMS, Kyoto Univ., 31 (1995), 645-665.
8. S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), 321-332.
9. S. Klainerman, Global Existence of small amplitude solutions to nonlinear Klein-Gordon equations with small data in four space - time dimensions, Comm. Pure Appl. Math., 38 (1985), 631-641.
10. S. Klainerman, The null condition and global existence to nonlinear wave equations, Lectures in Applied Math., 23 (1986), 293-326.
11. S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math., 36 (1983), 133-141.
12. R. Kosecki, The unit condition and global existence for a class of nonlinear Klein-Gordon equations, J. Differential Equations, 100 (1992), 257-268.
13. K. Moriyama, Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension, to appear in Diff. Integral Eqs.
14. T. Ozawa, K. Tsutaya and 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.
15. J. Shatah, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations, 46 (1982), 409-425.
16. J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math., 38 (1985), 685-696.
17. J. C. H. Simon and E. Taflin, The Cauchy problem for non-linear Klein-Gordon equations, Commun. Math. Phys., 152 (1993), 433-478.
18. K. Yagi, Normal forms and nonlinear Klein-Gordon equations in one space dimension, Master thesis, Waseda University, March (1994).
19. B. Yordanov, Blow-up for the one dimensional Klein-Gordon equation with a cubic nonlinearity, preprint.