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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of strong travelling wave profiles to $ 2\times 2$ systems of viscous conservation laws


Authors: Tong Yang, Mei Zhang and Changjiang Zhu
Journal: Proc. Amer. Math. Soc. 135 (2007), 1843-1849
MSC (2000): Primary 35L65; Secondary 74J30, 35L45
Published electronically: January 5, 2007
MathSciNet review: 2286095
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Abstract: In this paper, we prove the existence of strong travelling wave profiles for a class of $ 2\times 2$ viscous conservation laws when the corresponding invisid systems are hyperbolic. Besides some technical assumptions, the only main assumption is the hyperbolicity. Therefore, the existence theory can be applied to systems which are not strictly hyperbolic. Moreover, the characteristic fields can be neither genuinely nonlinear nor linearly degenerate.


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Additional Information

Tong Yang
Affiliation: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Email: matyang@cityu.edu.hk

Mei Zhang
Affiliation: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Email: meizhang3@student.cityu.edu.hk

Changjiang Zhu
Affiliation: Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People’s Republic of China
Email: cjzhu@mail.ccnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08747-3
PII: S 0002-9939(07)08747-3
Keywords: Viscous conservation laws, travelling wave profile, {\it a priori} estimate.
Received by editor(s): September 14, 2005
Received by editor(s) in revised form: February 13, 2006
Published electronically: January 5, 2007
Communicated by: Walter Craig
Article copyright: © Copyright 2007 American Mathematical Society