We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period 2π/ω and amplitude ∈. We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters (ω, ∈) in a Cantor set with asymptotically full measure as ∈ → 0.
Periodic solutions of forced Kirchhoff equations / Baldi, Pietro. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 8:1(2009), pp. 117-141. [10.2422/2036-2145.2009.1.06]
Periodic solutions of forced Kirchhoff equations
BALDI, PIETRO
2009
Abstract
We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period 2π/ω and amplitude ∈. We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters (ω, ∈) in a Cantor set with asymptotically full measure as ∈ → 0.File | Dimensione | Formato | |
---|---|---|---|
Baldi-Annali-Pisa-2009.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Dominio pubblico
Dimensione
166.5 kB
Formato
Adobe PDF
|
166.5 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Baldi-Annali-Pisa-2009.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Accesso privato/ristretto
Dimensione
166.5 kB
Formato
Adobe PDF
|
166.5 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.