Hyperbolic conservation laws with umbilic degeneracy (Q5957111)

The authors extend their earlier compactness framework to some canonical classes of quadratic flux systems with an isolated ombilic point. Using these topological arguments, they establish: (1) the compactness of the solution operator, (2) the long time behaviour in \(L^{\infty}\) of entropy solutions corresponding to large initial data, (3) the convergence of the vanishing viscosity method, of the Lax-Friedrichs scheme and of the Godunov scheme.