The Riemann Problem for Weakly Perturbed 2 × 2 Hyperbolic Systems

The Cauchy problem for a strictly hyperbolic system of two quasilinear equations with weak perturbation is considered. The asymptotics with respect to a small parameter for a discontinuous solution of the nonperturbed problem is studied. Complete asymptotic expansions are constructed if the solution of the nonperturbed problem involves two shock waves. Bibliography: 4 titles.