Global Classical Discontinuous Solutions to the Generalized Riemann Problem for Linearly Degenerate Hyperbolic Conservation Laws under Small BV Perturbations of the Initial Data
In this paper, we prove the existence and uniqueness of global piecewise C1 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
The author is partly supported by NSFC (No. 70371025), the Scientific Research Foundation of the Ministry of Education of China (No. 02JA790014), the Natural Science Foundation of Fujian Province of China (No. 2009J01006), and the Science and Technology Developmental Foundation of Fuzhou University (No. 2004-XQ-16).