Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Wave-front tracking for the equations of isentropic gas dynamics

Author: Fumioki Asakura
Journal: Quart. Appl. Math. 63 (2005), 20-33
MSC (2000): Primary 35L65, 35L67; Secondary 76N10, 76N15
DOI: https://doi.org/10.1090/S0033-569X-04-00935-8
Published electronically: December 13, 2004
MathSciNet review: 2126567
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the $2 \times 2$ system of conservation laws of the form $v_t - u_x = u_t + p(v)_x =0, p = k^2v^{-\gamma} (\gamma \geq 1)$, which are the model equations of isentropic gas dynamics. Weak global in time solutions are obtained by Nishida-Smoller (CPAM 1973) provided $(\gamma - 1)$ times the total variation of the initial data is sufficiently small. The aim of this paper is to give an alternative proof by using the Dafermos-Bressan-Risebro wave-front tracking scheme. We obtain new estimates of the total amount of interactions, which also imply the asymptotic decay of the solution. The main idea is to define appropriate amplitude to the path that is a continuation of shock fronts.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35L65, 35L67, 76N10, 76N15

Retrieve articles in all journals with MSC (2000): 35L65, 35L67, 76N10, 76N15

Additional Information

Fumioki Asakura
Affiliation: Osaka Electro-Communication University, Neyagawa, Osaka 572-8530, Japan
Email: asakura@isc.osakac.ac.jp

DOI: https://doi.org/10.1090/S0033-569X-04-00935-8
Keywords: Conservation laws, shock wave, wave-front tracking
Received by editor(s): November 29, 2003
Published electronically: December 13, 2004
Dedicated: Dedicated to Professor Atsushi Yoshikawa on his sixtieth birthday
Article copyright: © Copyright 2004 Brown University

American Mathematical Society