LAUSR

The exact solutions to the Riemann problem for an inhomogeneous extended Chaplygin gas equations with friction are constructed explicitly. Compared to the homogeneous system, the Riemann solutions for the inhomogeneous one are no longer self-similar. Then, as the two exponents vanish wholly or partly, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves are identified and investigated. It is rigorously proved that as the pressure tends to a constant, the Riemann solutions of the inhomogeneous extended Chaplygin gas equations converge to those of the zero-pressure flow with a body force, while as the pressure approaches some special generalized Chaplygin gas, the Riemann solutions of the inhomogeneous extended Chaplygin gas equations tend to those of the generalized Chaplygin gas equations with the same source term.