Shock reflection for a system of hyperbolic balance laws

This paper concerns shock reflection for a system of hyperbolic balance laws in one space dimension. It is shown that the generalized nonlinear initial–boundary Riemann problem for a system of hyperbolic balance laws with nonlinear boundary conditions in the half space {(t, x) | t 0, x 0} admits a unique global piecewise C1 solution u = u(t, x) containing only shocks with small amplitude and this solution possesses a global structure similar to that of self-similar solution u = U(x t ) of the corresponding homogeneous Riemann problem, if each characteristic field with positive velocity is genuinely nonlinear and the corresponding homogeneous Riemann problem has only shocks but no centered rarefaction waves and contact discontinuities. This result is also applied to shock reflection for the flow equations of a model class of fluids with viscosity induced by fading memory. © 2008 Elsevier Inc. All rights reserved.