(untitled) (Journal of Partial Differential Equations, 2020)
In this paper we consider the unperturbatcd and perturbated Riemann problem for the damped quasiliuear hyperbolic system v_t - u_x = 0 u_t + p(v)_x = -αu, α > 0, p'(v < 0 with initial structure of two rarefaction waves or one rarefaction wave plus one shock wave. Under certain restrictions, it admits a unique global discontinuous solution in a class of piecewise continuous and piecewise smooth functions and keeps the initial structure. Moreover, the shock strength is found decaying exponentially due to damping for the later case.