EXISTENCE OF GLOBAL L∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE

doi:10.1016/S0252-9602(18)30790-2

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 889-897.doi: 10.1016/S0252-9602(18)30790-2

EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE

刘树君¹, 陈芳启^1,2, 王泽军¹

1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China;
2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

收稿日期:2017-03-14 出版日期:2018-06-25 发布日期:2018-06-25
作者简介:Shujun LIU,E-mail:numsharxy@126.com;Fangqi CHEN,E-mail:fangqichen@nuaa.edu.cn;Zejun WANG,E-mail:zjwang@fudan.edu.cn
基金资助:
This work was supported by the National Science Foundation of China (11572148, 11671193) and the National Research Foundation for the Doctoral Program of Higher Education of China (20133218110025).

EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE

Shujun LIU¹, Fangqi CHEN^1,2, Zejun WANG¹

1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China;
2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received:2017-03-14 Online:2018-06-25 Published:2018-06-25
Supported by:
This work was supported by the National Science Foundation of China (11572148, 11671193) and the National Research Foundation for the Doctoral Program of Higher Education of China (20133218110025).

摘要/Abstract

摘要：

In this article, we give the existence of global L^∞ bounded entropy solutions to the Cauchy problem of a generalized n×n hyperbolic system of LeRoux type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2×2 to n×n and more linearly degenerate characteristic fields emerged, and the emergence of singularity in the region {v₁=0} is another difficulty. We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy-entropy flux and BV estimates on viscous solutions.

关键词: Conservation laws, hyperbolic system, LeRoux type, viscosity method, compensated compactness

Abstract:

Key words: Conservation laws, hyperbolic system, LeRoux type, viscosity method, compensated compactness

刘树君, 陈芳启, 王泽军. EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE[J]. 数学物理学报(英文版), 2018, 38(3): 889-897.

Shujun LIU, Fangqi CHEN, Zejun WANG. EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE[J]. Acta mathematica scientia,Series B, 2018, 38(3): 889-897.

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EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE

EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE

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