## Advances in Differential Equations

- Adv. Differential Equations
- Volume 1, Number 5 (1996), 817-856.

### The Cauchy problem for a class of $2\times 2$ hyperbolic systems of conservation laws with unbounded propagation speed

Masao Yamazaki and Taeko Yamazaki

#### Abstract

This paper shows the existence of time-global continuous characteristic solutions of the Cauchy problem for a class of $2 \times 2$ weakly hyperbolic systems of conservation laws in one space dimension with possibly unbounded initial propagation speed, and gives a condition on the growth of the initial propagation speed necessary and sufficient for the uniqueness of continuous solutions.

#### Article information

**Source**

Adv. Differential Equations, Volume 1, Number 5 (1996), 817-856.

**Dates**

First available in Project Euclid: 25 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366896021

**Mathematical Reviews number (MathSciNet)**

MR1392007

**Zentralblatt MATH identifier**

0866.35068

**Subjects**

Primary: 35L65: Conservation laws

Secondary: 73C50

#### Citation

Yamazaki, Masao; Yamazaki, Taeko. The Cauchy problem for a class of $2\times 2$ hyperbolic systems of conservation laws with unbounded propagation speed. Adv. Differential Equations 1 (1996), no. 5, 817--856. https://projecteuclid.org/euclid.ade/1366896021