The transition of Riemann solutions of the modified Chaplygin gas equations with friction to the solutions of the Chaplygin gas equations

Abstract

AbstractWe are concerned with the transition of Riemann solutions of the modified Chaplygin gas equations with a source term to the corresponding solutions of the inhomogeneous Chaplygin gas system. Different from the homogeneous equations, the Riemann solutions of the inhomogeneous system are non self‐similar. As the parameter in the modified Chaplygin gas tends to zero, the behavior of the Riemann solutions is considered. The phenomenon of concentration and the formation of the delta shock wave are identified and analyzed systematically.