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

DOI10.1007/BF02384318zbMath1073.35145OpenAlexW1997716161MaRDI QIDQ1426910

Haruhisa Ishida, Nicola Orrù, Ferruccio Colombini

Publication date: 15 March 2004

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02384318

zbMATH Keywords

well-posednessGevrey classweak hyperbolicityLevi conditionLevi type condition

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15)

Related Items (13)

The global Cauchy problem for a vibrating beam equation ⋮ On weakly hyperbolic operators with non-regular coefficients and finite order degeneration. ⋮ Some well-posed Cauchy problem for second order hyperbolic equations with two independent variables ⋮ Well posedness under Levi conditions for a degenerate second order Cauchy problem ⋮ A degenerate hyperbolic equation under Levi conditions ⋮ A dyadic decomposition approach to a finitely degenerate hyperbolic problem ⋮ Propagation of singularities in the Cauchy problem for a class of degenerate hyperbolic operators ⋮ On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable ⋮ The Cauchy problem for finitely degenerate hyperbolic equations with polynomial coefficients ⋮ Some results on the well-posedness for systems with time dependent coefficients ⋮ On the Cauchy problem of degenerate hyperbolic equations ⋮ On a sharp Levi condition in Gevrey classes for some infinitely degenerate hyperbolic equations and its necessity ⋮ Energy estimate and fundamental solution for degenerate hyperbolic Cauchy problems

Cites Work

• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in \(t\) and degenerate in \(t=T\)
• The cauchy problem for weakly hyperbolic equations of second order
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