Displaying similar documents to “A KAM-theorem for some nonlinear partial differential equations”

Galerkin averaging method and Poincaré normal form for some quasilinear PDEs

Dario Bambusi (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We use the Galerkin averaging method to construct a coordinate transformation putting a nonlinear PDE in Poincaré normal form up to finite order. We also give a rigorous estimate of the remainder showing that it is small as a differential operator of very high order. The abstract theorem is then applied to a quasilinear wave equation, to the water wave problem and to a nonlinear heat equation. The normal form is then used to construct approximate solutions whose difference from true...