Global Classical Discontinuous Solutions to the Generalized Riemann Problem for Linearly Degenerate Hyperbolic Conservation Laws under Small BV Perturbations of the Initial Data

摘要

In this paper, we prove the existence and uniqueness of global piecewise C~1 solution containing only n contact discontinuities to a class of the generalized Riemann problem, which can be regarded as a small BV perturbation of the corresponding Riemann problem, for general n × n linearly degenerate quasilinear hyperbolic system of conservation laws; moreover, this solution has a global structure similar to the one of the self-similar solution u = U(x/t) to the corresponding Riemann problem. Our result indicates that this kind of Riemann solution u = U(x/t) mentioned above for general n×n quasilinear hyperbolic systems of conservation laws possesses a global nonlinear structure stability under a small BV perturbation of the Riemann initial data. Applications include the one-dimensional Born-Infeld system arising in the string theory and high energy physics.