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Dynamics of nonlinear PDEs

Course Type: 
PhD Course
Academic Year: 
2016-2017
Period: 
November-March
Duration: 
50 h
Description: 

We shall discuss the complex dynamics of Hamiltonian or reversible PDEs, like the NLS,  the Klein-Gordon equation, the wave equation in several dimension,the water waves equations of hydrodynamics, focusing on both chatotic and regular behaviour as the existence of quasi-periodic solutions.We shall discuss also long time existence results obtained by Birkhoff normal forms. We shall develop general tools of nonlinear analysis, like the Nash-Moser implicit function theorem and the theory of pseudo-differential operators.The first part of the course will present general tools of pseudo differential and para-differential  operator theory.

Location: 
A-133

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