A coupling between a 1D compressible-incompressible limit and the 1D p-system in the non smooth case

We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we prove the rigorous convergence for the compressible to incompressible limit of the coupled dynamic of the two fluids.