Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 44, Number 1 (2007), 121-137.
Second order weakly hyperbolic operators with coefficients sum of powers of functions
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.
Osaka J. Math., Volume 44, Number 1 (2007), 121-137.
First available in Project Euclid: 19 March 2007
Permanent link to this document
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. https://projecteuclid.org/euclid.ojm/1174324326