Normal forms and long time existence for semilinear Klein–Gordon equations. (English) Zbl 1178.35310
Summary: We present in this text two results of long time existence for solutions of nonlinear Klein–Gordon equations, obtained through normal forms methods. In particular, we indicate how these methods allow one to obtain almost global solutions for that equation on spheres, despite the fact that such solutions do not go to zero when times goes to infinity.
MSC:
35Q40 | PDEs in connection with quantum mechanics |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |