United Boundary‐Domain Integro‐Differential and Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity.

The mixed BVP for a compressible Stokes system of PDEs with variable viscosity is considered in a bounded domain of three dimensions. Based on a specially constructed parametrix (Levi function), the problem is reduced to the united boundary‐domain integro‐differential or integral equations (BDIDEs or BDIEs). The BDIDEs are to be supplemented by the original boundary conditions, thus constituting boundary‐domain integro‐differential problems (BDIDPs). The BDIDPs/BDIEs contain integral operators defined on the domain under consideration as well as potential‐type operators defined on open submanifolds of the boundary and acting on the trace and/or traction of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, equivalence of the BDIDPs/BDIEs to the original BVP, and invertibility of the associated operators are investigated in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]