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 [Tesi di dottorato] (Unpublished)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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