The global Cauchy problem for the non linear Klein-Gordon equation-II
Ginibre, J. ; Velo, G.
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), p. 15-35 / Harvested from Numdam
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Publié le : 1989-01-01
@article{AIHPC_1989__6_1_15_0,
     author = {Ginibre, Jean and Velo, Giorgio},
     title = {The global Cauchy problem for the non linear Klein-Gordon equation-II},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {S6},
     year = {1989},
     pages = {15-35},
     mrnumber = {984146},
     zbl = {0694.35153},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1989__6_1_15_0}
}

Ginibre, J.; Velo, G. The global Cauchy problem for the non linear Klein-Gordon equation-II. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989) pp. 15-35. http://gdmltest.u-ga.fr/item/AIHPC_1989__6_1_15_0/

[1] J. Bergh and J. Löfström, Interpolation Spaces, Berlin-Heidelberg-New York, Springer, 1976. | MR 482275 | Zbl 0344.46071

[2] P. Brenner, On Lp-Lp, Estimates for the Wave Equation, Math. Z., Vol. 145, 1975, pp. 251-254. | MR 387819 | Zbl 0321.35052

[3] P. Brenner, On the Existence of Global Smooth Solutions of Certain Semi-Linear Hyperbolic Equations, Math. Z., Vol. 167, 1979, pp. 99-135. | MR 534820 | Zbl 0388.35048

[4] P. Brenner and W. Von WAHL, Global Classical Solutions of Non-Linear Wave Equations, Math. Z., Vol. 176, 1981, pp. 87-121. | MR 606174 | Zbl 0457.35059

[5] P. Brenner, Space-Times Means and Nonlinear Klein-Gordon Equations, Preprint.

[6] F.E. Browder, On Nonlinear Wave Equations, Math. Z., Vol. 80, 1962, pp. 249-264. | MR 147769 | Zbl 0109.32102

[7] J. Ginibre and G. Velo, The Global Cauchy Problem for the Nonlinear Klein-Gordon Equation, Math. Z., Vol. 189, 1985, pp. 487-505. | MR 786279 | Zbl 0549.35108

[8] R. Glassey and M. Tsutsumi, On Uniqueness of Weak Solutions to Semi-Linear Wave Equations, Commun. Partial Differ. Equations, Vol. 7, 1982, pp. 153-195. | MR 646135 | Zbl 0503.35059

[9] E. Heinz and W. Von WAHL, Zu einem Satz von F. E. Browder über nichtlineare Wellengleichungen, Math. Z., Vol. 141, 1975, pp. 33-45. | MR 365257 | Zbl 0282.35068

[10] K. Jörgens, Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen, Math. Z., Vol. 77, 1961, pp. 295-308. | MR 130462 | Zbl 0111.09105

[11] T. Kato, On Nonlinear Schrödinger Equations, Ann. I.H.P. (Phys. Theor.), Vol. 46, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[12] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Paris, Dunod - Gauthiers-Villars, 1969. | MR 259693 | Zbl 0189.40603

[13] B. Marshall, W. Strauss and S. Wainger, Lp-Lq Estimates for the Klein-Gordon Equation, J. Math. Pur. Appl., Vol. 59, 1980, pp. 417-440. | MR 607048 | Zbl 0457.47040

[14] C. Parenti, F. Strocchi and G. Velo, A Local Approach to Some Nonlinear Evolution Equations of Hyperbolic Type, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV, Ser. 3, 1976, pp. 443-500. | Numdam | MR 477483 | Zbl 0332.35040

[15] H. Pecher, Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I, Math. Z., Vol. 150, 1976, pp. 159-183. | MR 435604 | Zbl 0318.35054

[16] H. Pecher, Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen, Math. Z., Vol. 161, 1978, pp. 9-40. | MR 499812 | Zbl 0384.35039

[17] H. Pecher, Nonlinear Small Data Scaterring for the Wave and Klein-Gordon Equation, Math. Z., Vol. 185, 1984, pp. 261-270. | MR 731347 | Zbl 0538.35063

[18] H. PecherLow Energy Scattering for Nonlinear Klein-Gordon Equations, J. Funct. Anal., Vol. 63, 1985, pp. 101-122. | Zbl 0588.35061

[19] J.C. Peral, Lp-Estimates for the Wave Equation, J. Funct. Anal., Vol. 36, 1980, pp. 114-145. | MR 568979 | Zbl 0442.35017

[20] M. Reed, Abstract Nonlinear Wave Equations, Berhng-Heidelberg-New York, Springer, 1976.

[21] I.E. Segal, The Global Cauchy Problem for a Relativistic Scalar Field with Power Interaction, Bull. Soc. Math. Fr., Vol. 91, 1963, pp. 129-135. | Numdam | MR 153967 | Zbl 0178.45403

[22] 1. E. Segal, Nonlinear Semigroups, Ann. Math., Vol. 78, 1963, pp. 339-364. | Zbl 0204.16004

[23] I.E. Segal, Space-Time Decay for Solutions of Wave Equations, Adv. Math., Vol. 22, 1976, p. 305-311. | MR 492892 | Zbl 0344.35058

[24] W. Strauss, Decay and Asymptotics for ⊑u=f(u), J. Funct. Anal., Vol. 2, 1968, pp. 409-457. | MR 233062 | Zbl 0182.13602

[25] W. Strauss, On Weak Solutions of Semilinear Hyperbolic Equations, An. Acad. Bras. Cienc., Vol. 42, 1970, pp. 645-651. | MR 306715 | Zbl 0217.13104

[26] W. Strauss, Nonlinear Scattering Theory at Low Energy, J. Funct. Anal., Vol. 41, 1981, pp. 110-133. Ibid., Vol. 43, 1981, pp. 281-293. | MR 614228 | Zbl 0466.47006

[27] R. Strichartz, Convolutions with Kernels Having Singularities on a Sphere, Trans. Amer. Math. Soc., Vol. 148, 1970, pp. 461-470. | MR 256219 | Zbl 0199.17502

[28] R. Strichartz, Restrictions of Fourier Transforms to Quadratic Surfaces and Decay of Solutions of Wave Equations, Duke Math. J., Vol. 44, 1977, pp. 705-714. | MR 512086 | Zbl 0372.35001

[29] H. Triebel, Theory of Function Spaces, Basel, Birkhäuser, 1983. | Zbl 0546.46027

[30] W. Von Wahl, Klassische Lösungen nichtlinearer Wellengleichungen im Grossen, Math. Z., Vol. 112, 1969, pp. 241-279. | MR 280892 | Zbl 0177.36602

[31] W. Von Wahl, Uber nichtlineare Wellengleichungen mit zeitabhängigem elliptischem Hauptteil, Math. Z., Vol. 142, 1975, pp. 105-120. | MR 367470 | Zbl 0299.35064