Delta shock profiles for the pressureless two-phase flow model with the damping mechanism

The Riemann problem for the nonhomogeneous pressureless model of two-phase flow with the frictional damping term was considered by using two different methods for comparison. The Sarrico's theory of distributional products is first used to solve this problem in the frame of α–solutions on account of the defined solution concept in the context of distributional products. Two kinds of discontinuous solutions are achieved within a convenient space of distributions involving step-like functions and Dirac delta measures. Then, the substitution of the velocity variable is also used to find exact Riemann solutions for this nonhomogeneous model in perfectly explicit expressions, which may involve either a vacuum state or a delta shock wave. It is interestingly found that the strength and wave speed of this delta shock wave change exponentially with time under the influence of the frictional damping term.