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

Abstract

In this paper we study a non strictly system of conservation law when viscosity is present and viscosity is zero, which is studied in [10]. 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 [5] and Volpert product which was partly determined as vanishing viscosity limit in [10].