Delta shock waves as limits of vanishing viscosity for a 3×33× 3 pressureless gas dynamics model with composite source terms

The delta shock wave for a inhomogeneous pressureless gas dynamics model with time‐dependent composite source terms consisting of friction and damping is studied. It is found that the solutions are no longer self‐similar under the influence of the source terms. Thus, a general time‐dependent similar variable is proposed so that the delta‐shock solution is constructed by employing the vanishing viscosity approach. This will provide valuable insights on the vanishing viscosity limit of solutions to the conservation laws with complicated source terms. Finally, three typical examples with strong physical backgrounds are presented and the numerical results coinciding with the theoretical analysis are exhibited.