Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations

 Access to full text

 Full (PDF)

1. [1] J. Bergh, J. Löfström, Interpolation Spaces, Springer, Berlin, 1976. Zbl0344.46071MR482275
2. [2] M.S. Birman, M.Z. Solomjak, Vest. LSU, t. 24, 1969 ; translation : Vest. LSU Math., t. 2, 1975, p. 9-27. MR246163
3. [3] P. Brenner, Math. Scand., t. 51, 1982, p. 333-360. Zbl0517.35011MR690536
4. [4] P. Brenner, Math. Z., t. 186, 1984, p. 383-391. Zbl0524.35084MR744828
5. [5] P. Brenner, J. Diff. Eq., t. 56, 1985, p. 310-344. Zbl0513.35066MR780495
6. [6] P. Brenner, private communication. 
7. [7] J. Ginibre, G. Velo, J. Funct. Anal., t. 32, 1979, p. 1-32. Zbl0396.35028MR533219
8. [8] J. Ginibre, G. Velo, J. Funct. Anal., t. 32, 1979, p. 33-71. Zbl0396.35029MR533219
9. [9] J. Ginibre, G. Velo, Ann. IHP (Anal. non lin.), t. 2, 1985, p. 309-327. Zbl0586.35042MR801582
10. [10] J. Ginibre, G. Velo, Math. Z., t. 189, 1985, p. 487-505. Zbl0549.35108MR786279
11. [11] J. Ginibre, G. Velo, J. Math. Pur. Appl., in press. 
12. [12] L. Hörmander, The analysis of linear partial differential operators I, Springer, Berlin, 1983. Zbl0521.35001MR705278
13. [13] J.E. Lin, W. Strauss, J. Funct. Anal., t. 30, 1978, p. 245-263. Zbl0395.35070MR515228
14. [14] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod andGauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
15. [15] C. Morawetz, W. Strauss, Comm. Pure Appl. Math., t. 25, 1972, p. 1-31. Zbl0228.35055MR303097
16. [16] H. Pecher, Math. Z., t. 136, 1974, p. 67-92. Zbl0269.35059MR340825
17. [17] H. Pecher, Math. Z., t. 185, 1984, p. 245-263. 
18. [18] H. Pecher, J. Funct. Anal., t. 63, 1985, p. 101-122. Zbl0588.35061MR795519
19. [19] W. Strauss, J. Funct. Anal., t. 41, 1981, p. 110-133. Zbl0466.47006MR614228
20. [20] W. Strauss, J. Funct. Anal., t. 43, 1981, p. 281-293. Zbl0494.35068MR636702
21. [21] Y. Tsutsumi, Global existence and asymptotic behaviour of solutions for nonlinear Schrödinger equations, Thesis, Tokyo, 1984. 
22. [22] Y. Tsutsumi, Ann. IHP (Phys. Theor.), t. 43, 1985, p. 321-347. Zbl0612.35104MR824843
23. [23] M. Tsutsumi, J. Math. Soc. Japan, t. 35, 1983, p. 521-538. Zbl0554.35095MR702775
24. [24] M. Tsutsumi, N. Hayashi, Scattering of solutions of nonlinear Klein-Gordon Equations in higher space dimensions. Nonlinear PDE '83 Proceedings, Lecture Notes in numerical and applied analysis, Vol. 6, North-Holland. Zbl0566.35078MR839278

1. Pierre Germain, Global existence for coupled Klein-Gordon equations with different speeds
2. Alain Bachelot, Convergence dans $L^p\left(R^{n+1}\right)$ de la solution de l’équation de Klein-Gordon vers celle de l’équation des ondes
3. T. Ozawa, K. Tsutaya, Y. Tsutsumi, Normal form and global solutions for the Klein-Gordon-Zakharov equations
4. J. Ginibre, T. Ozawa, G. Velo, On the existence of the wave operators for a class of nonlinear Schrödinger equations
5. J. Ginibre, G. Velo, Conformal invariance and time decay for non linear wave equations. II
6. Jean Ginibre, Théorie de la diffusion pour des équations semi linéaires
7. Claude Zuily, Solutions en grand temps d'équations d'ondes non linéaires