## Tsukuba Journal of Mathematics

- Tsukuba J. Math.
- Volume 39, Number 1 (2015), 121-163.

### On the Cauchy problem for a class of hyperbolic operators whose coefficients depend only on the time variable

#### Abstract

In this paper we investigate the Cauchy problem for hyperbolic operators with double characteristics and hyperbolic operators of third order whose coefficients depend only on the time variable. And we give sufficient conditions for $C^{\infty}$ well-posedness.

#### Article information

**Source**

Tsukuba J. Math., Volume 39, Number 1 (2015), 121-163.

**Dates**

First available in Project Euclid: 7 August 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.tkbjm/1438951820

**Digital Object Identifier**

doi:10.21099/tkbjm/1438951820

**Mathematical Reviews number (MathSciNet)**

MR3383881

**Zentralblatt MATH identifier**

1336.35213

**Subjects**

Primary: 35L30: Initial value problems for higher-order hyperbolic equations

Secondary: 35L25: Higher-order hyperbolic equations

**Keywords**

Cauchy problem hyperbolic $C^{\infty}$ well-posed double characteristics third order

#### Citation

Wakabayashi, Seiichiro. On the Cauchy problem for a class of hyperbolic operators whose coefficients depend only on the time variable. Tsukuba J. Math. 39 (2015), no. 1, 121--163. doi:10.21099/tkbjm/1438951820. https://projecteuclid.org/euclid.tkbjm/1438951820