Global existence to the Cauchy problem for hyperbolic conservation laws with an isolated umbilic point
In this paper the existence of global weak solutions for a 2 × 2 system of non-strictly hyperbolic non-linear conservation laws is established for data in L∞. The result is proven by means of viscous approximation and application of the compensated compactness method. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain an existence result. For this purpose we combine the classical techniques referring to a singular EulerPoisson-Darboux equation with the compensated compactness method.