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

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 $$\varepsilon ^{-2}.$$

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
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