Hyperbolic Conservation Laws¶with Umbilic Degeneracy

Abstract

We continue to study hyperbolic systems of conservation laws with umbilic degeneracy. We further extend our compactness framework established earlier to other canonical classes of quadratic flux systems with an isolated umbilic point. With the aid of this compactness framework, we establish the compactness of solution operators and the long-time behavior of entropy solutions in L ^∞ with large initial data, and we prove the convergence of the viscosity method, as well as the Lax-Friedrichs scheme and the Godunov scheme, for a canonical class of nonlinear hyperbolic systems with umbilic degeneracy.