The generalized nonlinear initial–boundary Riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws

This work is a continuation of our previous work, in the present paper we study the generalized nonlinear initial–boundary Riemann problem with small BV data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space { ( t , x ) | t ⩾ 0 , x ⩾ 0 } . We prove the global existence and uniqueness of piecewise C 1 solution containing only contact discontinuities 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, 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 nonlinear initial–boundary Riemann problem. Some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given.