Dependence on the domain of solutions to a boundary value problem for the equations of mixtures of compressible viscous fluids

We study the dependence of solutions to an inhomogeneous boundary value problem for the equations of mixtures of compressible viscous fluids on the shape of the flow domain. The results can be used to prove the differentiability of the solutions and functionals of the solutions (for example, the drag functional) with respect to the parameter defining the shape variations of an obstacle in the flow.