## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Volume 4, Number 1 (2000), 105-117.

### KINETIC CONDITION AND THE GIBBS FUNCTION

#### Abstract

We study the Cauchy problem for a $3\times 3$-system of conservation laws describing the phase transition: $u_t-v_x=0$, $v_t-\sigma(u)_x=0$, $(e+\frac{1}{2}v^2)_t-(\sigma v)_x=0$. A phase boundary is said to be admissible if it satisfies the Abeyaratne-Knowles kinetic condition. We give a physical account of the kinetic condition by means of the $Gibbs function$. We also obtain a useful description of the entropy function using the Gibbs function.

#### Article information

**Source**

Taiwanese J. Math., Volume 4, Number 1 (2000), 105-117.

**Dates**

First available in Project Euclid: 18 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1500407200

**Digital Object Identifier**

doi:10.11650/twjm/1500407200

**Mathematical Reviews number (MathSciNet)**

MR1757985

**Zentralblatt MATH identifier**

0951.35078

**Subjects**

Primary: 35L65: Conservation laws 35L67: Shocks and singularities [See also 58Kxx, 76L05] 35L45: Initial value problems for first-order hyperbolic systems

**Keywords**

hyperbolic system conservation law phase boundary entropy

#### Citation

Asakura, Fumioki. KINETIC CONDITION AND THE GIBBS FUNCTION. Taiwanese J. Math. 4 (2000), no. 1, 105--117. doi:10.11650/twjm/1500407200. https://projecteuclid.org/euclid.twjm/1500407200