We study the dynamics of Hamiltonian quasilinear PDEs close to elliptic equilibria. Under a suitable nonresonance condition we prove an averaging theorem according to which any solution corresponding to smooth initial data with small amplitude remains very close to a torus up to long times. An application to quasilinear wave equations in an n-dimensional paralleliped is given.
An averaging theorem for quasilinear Hamiltonian PDEs / Dario Bambusi. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 4:4(2003), pp. 685-712.. [10.1007/s00023-003-0144-6]
An averaging theorem for quasilinear Hamiltonian PDEs.
Dario Bambusi
2003
Abstract
We study the dynamics of Hamiltonian quasilinear PDEs close to elliptic equilibria. Under a suitable nonresonance condition we prove an averaging theorem according to which any solution corresponding to smooth initial data with small amplitude remains very close to a torus up to long times. An application to quasilinear wave equations in an n-dimensional paralleliped is given.
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