EXISTENCE OF GLOBAL L&infin; SOLUTIONS TO A GENERALIZED n&times;n HYPERBOLIC SYSTEM OF LEROUX TYPE

Shujun LIU; Fangqi CHEN; Zejun WANG

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

Acta mathematica scientia, Series B >

2018 , Vol. 38 >Issue 3: 889 - 897

DOI: https://doi.org/10.1016/S0252-9602(18)30790-2

Articles

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

Shujun LIU ,
Fangqi CHEN ,
Zejun WANG

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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 date: 2017-03-14

Online 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).

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Abstract

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.

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

Cite this article

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 . DOI: 10.1016/S0252-9602(18)30790-2

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