Taiwanese Journal of Mathematics

KINETIC CONDITION AND THE GIBBS FUNCTION

Fumioki Asakura

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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


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