Hyperbolic conservation laws with umbilic degeneracy, I.

In this paper a compactness framework for approximate solutions to nonlinear hyperbolic systems with umbilic degeneracy is established by combining techniques of compensated compactness with some classical methods, and by a detailed analysis of a highly singular equation of Euler-Poisson-Darboux type. Then this framework is successfully applied to prove the convergence of the viscosity method and to prove the existence of global entropy solutions for the Cauchy problem with large initial data for a canonical class of the systems with quadratic flux form. [ABSTRACT FROM AUTHOR]