Osaka Journal of Mathematics

Second order weakly hyperbolic operators with coefficients sum of powers of functions

Ferruccio Colombini and Tatsuo Nishitani

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Abstract

We consider the Cauchy problem for the operator $D_t^2-D_xa(t,x)D_x$ in the Gevrey classes. We show that if the coefficient $a(t,x)$ is given by a finite sum of non negative functions then the Cauchy problem is well posed in the wider Gevrey class for the larger powers. We also give an example showing that the order of the Gevrey class obtained here is optimal.

Article information

Source
Osaka J. Math., Volume 44, Number 1 (2007), 121-137.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1174324326

Mathematical Reviews number (MathSciNet)
MR2313030

Zentralblatt MATH identifier
1124.35045

Subjects
Primary: 35L80: Degenerate hyperbolic equations
Secondary: 35L15: Initial value problems for second-order hyperbolic equations

Citation

Colombini, Ferruccio; Nishitani, Tatsuo. Second order weakly hyperbolic operators with coefficients sum of powers of functions. Osaka J. Math. 44 (2007), no. 1, 121--137. https://projecteuclid.org/euclid.ojm/1174324326


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References

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