Skip to main content
Log in

A dyadic decomposition approach to a finitely degenerate hyperbolic problem

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

We use the Littlewood-Paley decomposition technique to obtain a C-well-posedness result for a weakly hyperbolic equation with a finite order of degeneration.

Keywords: Littlewood-Paley decomposition, Hyperbolic equations, C-well-posedness, Approximate energy method

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 1. Ascanelli, A., Cicognani, M.: Energy estimate and fundamental solution for degenerate hyperbolic Cauchy problems. To appear in J. Differential Equations (2006)

  • 2. Bony, J.M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4) 14, no. 2, 209–246 (1981)

  • 3. Colombini, F., De Giorgi, E., Spagnolo, S.: Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 6, no. 3, 511–559 (1979)

  • 4. Colombini, F., Del Santo, D.: Strictly hyperbolic operators and approximate energies. Analysis and applications–ISAAC 2001 (Berlin), 253–277, Int. Soc. Anal. Appl. Comput. 10, Kluwer Acad. Publ., Dordrecht (2003)

  • 5. Colombini, F., Di Flaviano, M., Nishitani, T.: On the Cauchy problem for a weakly hyperbolic operator: an intermediate case between effective hyperbolicity and Levi condition. Partial differential equations and mathematical physics, Tokyo, (2001), 73–83, Progr. Nonlinear Differential Equations Appl. 52, Birkhäuser, Boston (2003)

  • 6. Colombini, F., Ishida, H., Orrù, N.: On the Cauchy problem for finitely degenerate hyperbolic equations of second order. Ark. Mat. 38, no. 2, 223–230 (2000)

    Google Scholar 

  • 7. Colombini, F., Jannelli, E., Spagnolo, 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. (4) 10, no. 2, 291–312 (1983)

  • 8. Colombini, F., Lerner, N.: Hyperbolic operators with non-Lipschitz coefficients. Duke Math. J. 77, no. 3, 657–698 (1995)

  • 9. Colombini, F., Nishitani, T.: On finitely degenerate hyperbolic operators of second order. Osaka J. Math. 41, no. 4, 933–947 (2004)

    Google Scholar 

  • 10. Del Santo, D., Kinoshita, T., Reissig, M.: Energy estimates for strictly hyperbolic equations with low regularity in coefficients. To appear (2006)

  • 11. Nishitani, T.: The Cauchy problem for weakly hyperbolic equations of second order. Comm. Partial Differential Equations 5, no. 12, 1273–1296 (1980)

    Google Scholar 

  • 12. Nishitani, T.: The effectively hyperbolic Cauchy problem. The hyperbolic Cauchy problem (by K. Kajitani and T. Nishitani), 71–167, Lecture Notes in Mathematics 1505, Springer-Verlag, Berlin (1991)

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

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cicognani, M., Santo, D.D. & Reissig, M. A dyadic decomposition approach to a finitely degenerate hyperbolic problem. Ann. Univ. Ferrara 52, 281–289 (2006). https://doi.org/10.1007/s11565-006-0021-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-006-0021-6

Navigation