Data di Pubblicazione:
2003
Citazione:
Birkhoff normal form for some nonlinear PDEs / Dario Bambusi. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 234:2(2003), pp. 253-285..
Abstract:
We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation
utt-uxx+g(x,u)=0,
0.1
with Dirichlet boundary conditions on [0,?]; g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2? in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
Dario Bambusi
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