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 Le Roux 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.
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 Le Roux 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.
作者
刘树君
陈芳启
王泽军
Shujun LIU;Fangqi CHEN;Zejun WANG(Department of Mathematics,College of Science,Nanjing University of Aeronautics and Astronautic;College of Mathematics and Systems Science,Shandong University of Science and Technolog)
基金
supported by the National Science Foundation of China(11572148,11671193)
the National Research Foundation for the Doctoral Program of Higher Education of China(20133218110025)
