## Differential and Integral Equations

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

Alessia Ascanelli

#### 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

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