Skip to main content
SpringerLink
Log in

On the Cauchy problem for finitely degenerate hyperbolic equations of second order

  • Published:
Arkiv för Matematik

Abstract

This paper is devoted to the study of the Cauchy problem inC ∞ and in the Gevrey classes for some second order degenerate hyperbolic equations with time dependent coefficients and lower order terms satisfying a suitable Levi condition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [CDS]Colombini, F., De Giorgi, E. andSpagnolo, S., Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps,Ann. Scuola Norm. Sup. Pisa Cl. Sci. 6 (1979), 511–559.

    MathSciNet  Google Scholar 

  • [CJS]Colombini, F., Jannelli, E. andSpagnolo, S., Well-posedness in Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time,Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (1983), 291–312.

    MathSciNet  Google Scholar 

  • [CS]Colombini, F. andSpagnolo, S., An example of a weakly hyperbolic Cauchy problem not well posed inC ∞,Acta Math. 148 (1982), 243–253.

    MathSciNet  Google Scholar 

  • [H]Hörmander, L.,The Analysis of Linear Partial Differential Operators I, 2nd ed., Grundlehren Math. Wiss.256, Springer-Verlag, Berlin-Heidelberg, 1990.

    Google Scholar 

  • [IO]Ishida, H. andOdai, H., The initial value problem for some degenerate hyperbolic equations of second order in Gevrey classes,Funkcial. Ekvac. 43 (2000), 71–85.

    MathSciNet  Google Scholar 

  • [I]Ivrii, V. Ja., Cauchy problem conditions for hyperbolic operators with characteristics of variable multiplicity for Gevrey classes,Sibirsk. Mat. Zh. 17 (1976), 1256–1270, 1437 (Russian). English transl.:Siberian Math. J. 17 (1976), 921–931.

    MATH  MathSciNet  Google Scholar 

  • [K]Kinoshita, T., On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous int and degenerate int=T, Rend. Sem. Mat. Univ. Padova 100 (1998), 81–96.

    MATH  MathSciNet  Google Scholar 

  • [M]Mizohata, S.,On the Cauchy Problem, Notes and Reports in Math. in Sci. and Eng., Academic Press, Orlando, Fla.; Science Press, Beijing, 1985.

    Google Scholar 

  • [N1]Nishitani, T., The Cauchy problem for weakly hyperbolic equations of second order,Comm. Partial Differential Equations 5 (1980), 1273–1296.

    MATH  MathSciNet  Google Scholar 

  • [N2]Nishitani, T., The effectively hyperbolic Cauchy problem, inThe Hyperbolic Cauchy Problem (by Kajitani, K. and Nishitani, T.), Lecture Notes in Math.1505, pp. 71–167, Springer-Verlag, Berlin-Heidelberg, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, IT-56127, Pisa, Italy

    Ferruccio Colombini

  2. Institute of Mathematics, University of Tsukuba, 305-8571, Ibaraki, Japan

    Haruhisa Ishida

  3. Via Genova 5, IT-07100, Sassari, Italy

    Nicola Orrú

Authors
  1. Ferruccio Colombini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haruhisa Ishida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Orrú
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colombini, F., Ishida, H. & Orrú, N. On the Cauchy problem for finitely degenerate hyperbolic equations of second order. Ark. Mat. 38, 223–230 (2000). https://doi.org/10.1007/BF02384318

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384318

Keywords

Search

Navigation