The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a source term

The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a friction term is considered. Unlike the homogeneous case, the Riemann solutions are no longer self-similar due to the influence of the source term. In particular, delta contact discontinuities are found in the Riemann solutions with delta initial data for the Chaplygin gas equations with the source term. Moreover, we discover that the Chaplygin gas equations can be transformed to the equations of string motion in Minkowski space. The delta shock wave can explain the appearance of the singularities developed in the motion of the string.