CONSERVATION-LAWS POSSESSING CONTACT CHARACTERISTIC FIELDS WITH SINGULARITIES

In many applications, there arise systems of two nonlinear. conservati on laws with a single linearly degenerate characteristic field, or con tact field, the speed of which may coincide with that of the genuinely nonlinear characteristic field along a curve. Along this coincidence curve, the contact field may have isolated singular points. We prove t hat under generic assumptions the singular points can be centers or sa ddles for the contact field. We construct the local Riemann solution f or each of the two generic cases. This work sheds light on the classif ication of local Riemann solutions of systems of two conservation laws with a linearly degenerate characteristic field.