## Arkiv för Matematik

• Ark. Mat.
• Volume 49, Number 1 (2011), 109-127.

### Time regularity of the solutions to second order hyperbolic equations

#### 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.

#### Article information

Source
Ark. Mat., Volume 49, Number 1 (2011), 109-127.

Dates
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485907130

Digital Object Identifier
doi:10.1007/s11512-009-0120-6

Mathematical Reviews number (MathSciNet)
MR2784260

Zentralblatt MATH identifier
1211.35064

Rights

#### Citation

Kinoshita, Tamotu; Taglialatela, Giovanni. Time regularity of the solutions to second order hyperbolic equations. Ark. Mat. 49 (2011), no. 1, 109--127. doi:10.1007/s11512-009-0120-6. https://projecteuclid.org/euclid.afm/1485907130

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