Kelvin–Voigt equations characterized by abruptly changing density

Kelvin–Voigt equations for inhomogeneous fluids with a singular right side are studied. A singular term that approximates the Dirac delta function on an initially infinitely thin layer is introduced into the right side of a mass balance equation. This singular term is similar to the relaxation term used to describe nonequilibrium processes in hydrodynamics. In an extreme case, when a small parameter, namely the characteristic size of the initial layer, tends to zero, the density and velocity at the initial time change abruptly.