Delort, Jean-Marc:
Normal Forms and Long Time Existence for Semi-Linear Klein-Gordon Equations
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.1, p. 1-23, Unione Matematica Italiana (English)
pdf (478 Kb), djvu (221 Kb). | MR 2310955 | Zbl 1178.35310
Sunto
Presentiamo in questo testo due risultati di esistenza di lungo periodo per soluzioni di equazioni non lineari di Klein-Gordon, ottenuti mediante metodi di forme normali. In particolare indichiamo come questi metodi permettono di ottenere soluzioni quasi globali per tale equazione sulle sfere, a dispetto del fatto che tali soluzioni non tendono a zero quando il tempo tende ad infinito.
Referenze Bibliografiche
[2]
D. BAMBUSI -
J.-M. DELORT -
B. GRÉBERT -
J. SZEFTEL,
Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds, to appear,
Comm. Pure Appl. Math. |
fulltext (doi) |
MR 2349351 |
Zbl 1170.35481[6]
J.-M. DELORT,
Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1,
École Norm. Sup. (4)
34, no. 1 (
2001), 1-61.
Erratum,
Ann. Sci. École Nor. Sup. (4)
39, no.2 (2006), 335-345. |
fulltext EuDML |
fulltext (doi) |
MR 1833089 |
Zbl 0990.35119[7]
J.-M. DELORT -
D. FANG -
R. XUE,
Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions,
J. Funct. Anal.,
211, no. 2 (
2004), 288-323. |
fulltext (doi) |
MR 2056833 |
Zbl 1061.35089[8]
J.-M. DELORT -
J. SZEFTEL,
Long-time existence for small data nonlinear Klein-Gordon equations on tori and spheres,
Int. Math. Res. Not., no.
37 (
2004), 1897-1966. |
fulltext (doi) |
MR 2056326 |
Zbl 1079.35070[9]
J.-M. DELORT -
J. SZEFTEL,
Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds,
Amer. J. Math.,
128, no. 5 (
2006), 1187-1218. |
MR 2262173 |
Zbl 1108.58023[11] B. GRÉBERT, Birkhoff normal form and hamiltonian PDEs, preprint, (2006).
[12]
V. GUILLEMIN,
Lectures on spectral theory of elliptic operators,
Duke Math. J.,
44, no. 3 (
1977), 485-517. |
MR 448452 |
Zbl 0463.58024[13]
L. HÖRMANDER,
Lectures on nonlinear hyperbolic differential equations,
Mathématiques and Applications,
26,
Springer-Verlag, Berlin,
1997. viii+289 pp. |
MR 1466700[14]
S. KLAINERMAN,
Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions,
Comm. Pure Appl. Math.,
38, no. 5 (
1985), 631-641. |
fulltext (doi) |
MR 803252 |
Zbl 0597.35100[15]
H. LINDBLAD -
A. SOFFER,
A remark on Long Range Scattering for the critical nonlinear Klein-Gordon equation,
J. Hyperbolic Differ. Equ. 2, no. 1 (
2005), 77-89. |
fulltext (doi) |
MR 2134954 |
Zbl 1080.35044[16]
H. LINDBLAD -
A. SOFFER,
A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation,
Lett. Math. Phys.,
73, no. 3 (
2005), 249-258. |
fulltext (doi) |
MR 2188297 |
Zbl 1106.35072[17]
K. MORIYAMA -
S. TONEGAWA -
Y. TSUTSUMI,
Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension,
Funkcial. Ekvac.,
40, no. 2 (
1997), 313-333. |
MR 1480281 |
Zbl 0891.35142[18]
T. OZAWA -
K. TSUTAYA -
Y. TSUTSUMI,
Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions,
Math. Z.,
222, no. 3 (
1996), 341-362. |
fulltext EuDML |
fulltext (doi) |
MR 1400196 |
Zbl 0877.35030[20]
A. WEINSTEIN,
Asymptotics of eigenvalue clusters for the Laplacian plus a potential,
Duke Math. J.,
44, no. 4 (
1977), 883-892. |
MR 482878 |
Zbl 0385.58013
Con il contributo del Ministero per i Beni e le Attività Culturali