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