NON-CLASSICAL GENERALIZED SOLUTIONS FOR SOME HYPERBOLIC SYSTEMS

We consider some hyperbolic systems whose solutions are measures, not theusual functions under certain initial data. By introducing new methods which are generatedfrom a new notion on generalized solution, some results of existence and uniqueness ofentropy solution for these systems are obtained. In particular, our results include the caseof gas dynamical equations with zero pressure.Besides, we also investigate two-dimensional problems of conservation laws. For a specialhyperbolic system, we prove existence and uniqueness of solution, and for simplified Eulerequations, we construct solutions of Riemann problems where initial data have two differentconstant states which are separated by initial discontinuity. Some new phenomena of 2-Dsolutions are discovered.