Initial-boundary value problems for incomplete singular perturbations of hyperbolic systems

The present paper is concerned with a flow of a slightly viscous perfect gas. The flow is governed by the compressible Navier-Stokes equations. The dissipation function is considered, taking into account terms viewed as an incomplete elliptic perturbation of a system of hyperbolic equations. Questions are studied regarding the boundary conditions for which the solutions of the perturbed problem are well defined in some time interval. The limit of the solutions is also considered along with the asymptotics as a small parameter epsilon approaches zero.