Generalized solution to a system of conservation laws which is not strictly hyperbolic

In this paper we study a non-strictly hyperbolic system of conservation laws when viscosity is present and when viscosity is zero, which has been studied in [12]. We show the existence and uniqueness of the solution in the space of generalized functions of Colombeau for the viscous problem and construct a solution to the inviscid system in the sense of association. Also we construct a solution using shadow wave approach [17] and Volpert product which was partially determined as vanishing viscosity limit in [12].