Long-time existence for semi-linear beam equations on irrational tori. (English) Zbl 1482.35201
The semi-linear beam equation on the \(d\) dimensional irrational torus with smooth nonlinearity of order \(n-1\) with \(n \ge 3\) and \(d \ge 2\) has been studied and the lifespan of solutions is obtained for some small initial datum, which improves the time given by the local existence theory. The result is obtained by combining a Birkhoff normal form step and a modified energy step.
Reviewer: Long Wei (Hangzhou)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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