Differential and Integral Equations

The cauchy problem for a weakly hyperbolic equation with unbounded and non-Lipschitz-continuous coefficients

Alessia Ascanelli

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Abstract

We consider a second-order weakly hyperbolic equation with time and space depending coefficients. We suppose the coefficients to have globally a H\"older type behavior and locally a blow up of the first derivative at some time. We show that the Cauchy problem for such an equation is well posed in Gevrey classes $G^\sigma$; the upper bound for the Gevrey index $\sigma$ depends only on the dominant between the local and the global condition.

Article information

Source
Differential Integral Equations Volume 20, Number 4 (2007), 467-480.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039463

Mathematical Reviews number (MathSciNet)
MR2307143

Zentralblatt MATH identifier
1212.35282

Subjects
Primary: 35L15
Secondary: 35L80

Citation

Ascanelli, Alessia. The cauchy problem for a weakly hyperbolic equation with unbounded and non-Lipschitz-continuous coefficients. Differential Integral Equations 20 (2007), no. 4, 467--480. https://projecteuclid.org/euclid.die/1356039463.


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