## Advances in Differential Equations

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

#### 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