Wen Shen, Penn State University
601, Pao Yue-Kong Library
A main building block for the analysis of hyperbolic conservation laws is the solution of the Riemann problem, where the initial data are piecewise constant. In general, when the flux is nonlinear and the system is hyperbolic, solutions for Riemann problems only exist for initial data where the jump is sufficiently small. In this talk we consider several 3x3 systems, some from reservoir simulation and some from traffic flow, with parabolic degeneracy. Thanks to special features in the models, we can construct global Riemann solvers. Further research topics for these equations will also be discussed.