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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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

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

First available in Project Euclid: 19 March 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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