Well-posedness for a class of $n\times n$ hyperbolic systems and shock stability for the viscous approximation

We establish the global well-posedness of weak solutions to the Cauchy problem for a broad class of multi-dimensional $n\times n$ Keyfitz-Kranzer type systems with homogeneous flux. Our proof relies on a novel viscous approximation that yields the necessary compactness estimates. By exploiting the s