Birfhoff Normal Form for PDEs with Tame Modulus
| dc.creator | Bambusi, D. | |
| dc.creator | Grebert, B. | |
| dc.date | 2004-11-03 | |
| dc.date.accessioned | 2026-07-07T04:31:35Z | |
| dc.date.available | 2026-07-07T04:31:35Z | |
| dc.description | We prove an abstract Birkhoff normal form theorem for Hamiltonian Partial Differential Equations. The theorem applies to semilinear equations with nonlinearity satisfying a property that we call of Tame Modulus. Such a property is related to the classical tame inequality by Moser. In the nonresonant case we deduce that any small amplitude solution remains very close to a torus for very long times. We also develop a general scheme to apply the abstract theory to PDEs in one space dimensions and we use it to study some concrete equations (NLW,NLS) with different boundary conditions. An application to a nonlinear Schrödinger equation on the $d$-dimensional torus is also given. In all cases we deduce bounds on the growth of high Sobolev norms. In particular we get lower bounds on the existence time of solutions. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0411011 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0411011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57870 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.title | Birfhoff Normal Form for PDEs with Tame Modulus | |
| dc.type | text |