Long-time existence for small data nonlinear Klein-Gordon equations on tori and spheres. (English) Zbl 1079.35070

Delort, J.-M.; Szeftel, J.

Int. Math. Res. Not. 2004, No. 37, 1897-1966 (2004).

The paper deals with long-time existence of solutions to quasilinear Klein-Gordon equations with small smooth initial data \(\varepsilon u_0,\varepsilon u_1\) on compact manifolds, namely tori and spheres. It is proved, that time of existence to smooth solutions tends to infinity as at least \(\varepsilon ^{-2}.\)

Reviewer: Marie Kopáčková (Praha)

MSC:

35L70	Second-order nonlinear hyperbolic equations
35L15	Initial value problems for second-order hyperbolic equations
35B65	Smoothness and regularity of solutions to PDEs
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

Fourier transform