RIEMANN SOLUTIONS WITHOUT INTERMEDIATE CONSTANT STATES FOR A SYSTEM OF CONSERVATION LAWS

摘要

We consider a nonlinear system of conservation laws arising in petroleum engineering. We are modeling the injection of a mixture of gas and oil, in any proportion, into a porous medium filled with a similar mixture. The two mixtures may have different temperatures. We will focus on a particularly unusual feature found in this model: for open set of Riemann data the solution is given by a single wave group, i.e., there is no constant intermediate state. The key aspect supporting this feature is the existence of structurally stable doubly sonic shock waves, which robustly connect slow rarefaction waves to fast rarefaction waves. The solutions are constructed around a curve of coinciding characteristic speeds, intrinsically associated to most bifurcations in the Riemann solutions for this class of models.