In a celebrated paper (Tokyo J. Math. 1984) Nishihara proved global existence for Kirchhoff equations in a special class of initial data which lies in between analytic functions and Gevrey spaces. This class was defined in terms of Fourier components with weights satisfying suitable convexity and integrability conditions. In this paper, we extend this result by removing the convexity constraint, and by replacing Nishihara's integrability condition with the simpler integrability condition which appears in the usual characterization of quasi-analytic functions. After the convexity assumptions have been removed, the resulting theory reveals unexpected connections with some recent global existence results for spectral-gap data.

Kirchhoff equations from quasi-analytic to spectral-gap data

GHISI, MARINA;GOBBINO, MASSIMO
2011-01-01

Abstract

In a celebrated paper (Tokyo J. Math. 1984) Nishihara proved global existence for Kirchhoff equations in a special class of initial data which lies in between analytic functions and Gevrey spaces. This class was defined in terms of Fourier components with weights satisfying suitable convexity and integrability conditions. In this paper, we extend this result by removing the convexity constraint, and by replacing Nishihara's integrability condition with the simpler integrability condition which appears in the usual characterization of quasi-analytic functions. After the convexity assumptions have been removed, the resulting theory reveals unexpected connections with some recent global existence results for spectral-gap data.
2011
Ghisi, Marina; Gobbino, Massimo
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/193804
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 16
social impact