02-437 Bambusi D.

Averaging Theorem for Quasilinear Hamiltonian PDEs in Arbitrary Space Dimensions (82K, TeX) Oct 28, 02

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Abstract. We study the dynamics of quasilinear Hamiltonian wave equations with Dirichlet boundary conditions in an $n$--dimensional parallepided. We prove an averaging theorem according to which the solution corresponding to an arbitrary small amplitude smooth initial datum remains arbitrarily close to a finite dimensional torus up to very long times. We expect the result to be valid for a very general class of quasilinear Hamiltonian equations.

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