03-130 Bambusi D.

An Averaging Theorem for Quasilinear Hamiltonian PDEs (81K, TeX) Mar 21, 03

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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 small amplitude smooth initial data remain 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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