In this paper we prove a well posed and an ill posed result in the Gevrey category for a simple model hyperbolic operator with triple characteristics, when the principal symbol cannot be smoothly factorized, and whose propagation cone is not transversal to the triple characteristic manifold, thus confirming the conjecture that the Ivrii-Petkov condition is not sufficient for the C∞ well posedness unless the propagation cone is transversal to the characteristic manifold, albeit for a limited class of operators. Moreover we are able not only to disprove C∞ well posedness, but we can actually estimate the precise Gevrey threshold where well posedness will cease to hold.

Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics / Bernardi, Enrico; Nishitani, Tatsuo. - In: PROCEEDINGS OF THE JAPAN ACADEMY. SERIES A MATHEMATICAL SCIENCES. - ISSN 0386-2194. - STAMPA. - 91:(2015), pp. 19-24. [10.3792/pjaa.91.19]

Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics

BERNARDI, ENRICO;
2015

Abstract

In this paper we prove a well posed and an ill posed result in the Gevrey category for a simple model hyperbolic operator with triple characteristics, when the principal symbol cannot be smoothly factorized, and whose propagation cone is not transversal to the triple characteristic manifold, thus confirming the conjecture that the Ivrii-Petkov condition is not sufficient for the C∞ well posedness unless the propagation cone is transversal to the characteristic manifold, albeit for a limited class of operators. Moreover we are able not only to disprove C∞ well posedness, but we can actually estimate the precise Gevrey threshold where well posedness will cease to hold.
2015
Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics / Bernardi, Enrico; Nishitani, Tatsuo. - In: PROCEEDINGS OF THE JAPAN ACADEMY. SERIES A MATHEMATICAL SCIENCES. - ISSN 0386-2194. - STAMPA. - 91:(2015), pp. 19-24. [10.3792/pjaa.91.19]
Bernardi, Enrico; Nishitani, Tatsuo
File in questo prodotto:
Eventuali allegati, non sono esposti

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/11585/507578
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact