ALMOST GLOBAL EXISTENCE OF CLASSICAL DISCONTINUOUS SOLUTIONS TO GENERAL QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SMALL BV INITIAL DATA

摘要

In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution only contains shocks and contact discontinuities, the perturbations are in BV but they are assumed to be C~1-smooth, with bounded and possibly large C~1-norms. The author obtains the almost global existence and lifespan of classical discontinuous solutions to a class of the generalized Riemann problem, which can be regarded as a small BV perturbation of the corresponding Riemann problem. Some applications to quasilinear hyperbolic systems of conservation laws arising in physics, particularly to one-dimensional compressible Euler equations, are also given.