LIFESPAN OF CLASSICAL DISCONTINUOUS SOLUTIONS TO THE GENERALIZED NONLINEAR INITIAL-BOUNDARY RIEMANN PROBLEM FOR HYPERBOLIC CONSERVATION LAWS WITH SMALL BV DATA: SHOCKS AND CONTACT DISCONTINUITIES

In the present paper the author investigates the generalized nonlinear initial-boundary Riemann problem with small BV data for general n x n quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space {(t, x)It >= 0, x >= 0}, where the Riemann solution only contains shocks and contact discontinuities. Combining the techniques employed by Li-Kong with the modified Glimm's functional, the author obtains the almost global existence and lifespan of classical discontinuous solutions to a class of the generalized nonlinear initial-boundary Riemann problem, which can be regarded as a small BV perturbation of the corresponding nonlinear initial-boundary Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw-Rascle model.