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AVERAGING THEOREM FOR QUASILINEAR HAMILTONIAN PDEs IN ARBITRARY SPACE DIMENSIONS

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.