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2007 The cauchy problem for a weakly hyperbolic equation with unbounded and non-Lipschitz-continuous coefficients
Alessia Ascanelli
Differential Integral Equations 20(4): 467-480 (2007).

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.

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Alessia Ascanelli. "The cauchy problem for a weakly hyperbolic equation with unbounded and non-Lipschitz-continuous coefficients." Differential Integral Equations 20 (4) 467 - 480, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35282
MathSciNet: MR2307143

Subjects:
Primary: 35L15
Secondary: 35L80

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 4 • 2007
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