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

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.