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April 2011 Time regularity of the solutions to second order hyperbolic equations
Tamotu Kinoshita, Giovanni Taglialatela
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Ark. Mat. 49(1): 109-127 (April 2011). DOI: 10.1007/s11512-009-0120-6

Abstract

We consider the Cauchy problem for a second order weakly hyperbolic equation, with coefficients depending only on the time variable. We prove that if the coefficients of the equation belong to the Gevrey class $\gamma^{s_{0}}$ and the Cauchy data belong to $\gamma^{s_{1}}$, then the Cauchy problem has a solution in $\gamma^{s_{0}}([0,T^{*}];\gamma^{s_{1}}(\mathbb{R}))$ for some T*>0, provided 1≤s1≤2−1/s0. If the equation is strictly hyperbolic, we may replace the previous condition by 1≤s1s0.

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Tamotu Kinoshita. Giovanni Taglialatela. "Time regularity of the solutions to second order hyperbolic equations." Ark. Mat. 49 (1) 109 - 127, April 2011. https://doi.org/10.1007/s11512-009-0120-6

Information

Received: 6 May 2009; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1211.35064
MathSciNet: MR2784260
Digital Object Identifier: 10.1007/s11512-009-0120-6

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 1 • April 2011
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