Magistrelli, Elisa (2011) KAM Theory for PDEs. [Tesi di dottorato] (Unpublished)

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Item Type: Tesi di dottorato
Resource language: English
Title: KAM Theory for PDEs
Creators:
Creators
Email
Magistrelli, Elisa
elisa.magistrelli@unina.it
Date: 30 November 2011
Number of Pages: 88
Institution: Università degli Studi di Napoli Federico II
Department: Matematica e applicazioni "Renato Caccioppoli"
Scuola di dottorato: Scienze matematiche e informatiche
Dottorato: Scienze matematiche
Ciclo di dottorato: 24
Coordinatore del Corso di dottorato:
nome
email
De Giovanni, Francesco
UNSPECIFIED
Tutor:
nome
email
Berti, Massimiliano
m.berti@unina.it
Date: 30 November 2011
Number of Pages: 88
Keywords: KAM, PDE, resonant, degenerate
Settori scientifico-disciplinari del MIUR: Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica
Date Deposited: 07 Dec 2011 14:25
Last Modified: 30 Apr 2014 19:49
URI: http://www.fedoa.unina.it/id/eprint/8986
DOI: 10.6092/UNINA/FEDOA/8986

Collection description

This thesis is concerned with KAM theory for Hamiltonian partial differential equations. This theory answers to the following matter: since the solutions of a linear equation are periodic, quasi periodic or almost periodic (for they are superpositions of periodic motions), the problem is to investigate what happens when we add a (sufficiently) small nonlinearity. This thesis contains two new results: an abstract KAM theorem for degenerate infinite--dimensional systems, with an application to the nonlinear wave equation, and a KAM theorem for a completely resonant nonlinear Schr\"odinger equation.

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