The local solvability of the Cauchy problem in Sobolev spaces is studied for a class of nonlinear p-evolution partial differential equations of order pm, p>1, with real characteristic roots in the principal part in the sense of Petrowski. The non real lower order terms do not exceed some order depending on the order of the operator in the time variable m, on the maximum multiplicity of the characteristic roots,r, and on the type of the evolution p ([2]). The paper extends both results concerning linear equations of p-evolution type, p>1 ( [12-15], [9],[1] ) to nonlinear ones and includes , if p=1, results concerning H^{s}-wellposedness for quasilinear weakly hyperbolic equations with characteristics of constant multiplicity [6].

Cauchy problem for nonlinear p-evolution equations

ZANGHIRATI, Luisa
2009

Abstract

The local solvability of the Cauchy problem in Sobolev spaces is studied for a class of nonlinear p-evolution partial differential equations of order pm, p>1, with real characteristic roots in the principal part in the sense of Petrowski. The non real lower order terms do not exceed some order depending on the order of the operator in the time variable m, on the maximum multiplicity of the characteristic roots,r, and on the type of the evolution p ([2]). The paper extends both results concerning linear equations of p-evolution type, p>1 ( [12-15], [9],[1] ) to nonlinear ones and includes , if p=1, results concerning H^{s}-wellposedness for quasilinear weakly hyperbolic equations with characteristics of constant multiplicity [6].
2009
R., Agliardi; Zanghirati, Luisa
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in SFERA 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/11392/1378678
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 8
social impact