  We show existence, uniqueness and stability for a family of stationary
subsonic compressible Euler flows with mass-additions in two-dimensional
rectilinear ducts, subjected to suitable time-independent multi-dimensional
boundary conditions at the entrances and exits.The stationary subsonic Euler
equations consist a quasi-linear system of elliptic-hyperbolic composite-mixed
type, while addition-of-mass destructs the usual methods based upon
conservation of mass and Lagrangian coordinates to separate the elliptical and
hyperbolic modes of the system. We establish a new decomposition and nonlinear
iteration scheme to overcome this major difficulty. It reveals that
mass-additions introduce very strong interactions in the elliptic and
hyperbolic modes, and lead to a class of second-order elliptic equations with
multiple integral nonlocal terms. The linearized problem is solved by studying
algebraicand analytical properties of infinite weakly coupled boundary-value
problems of ordinary differential equations, each with multiple nonlocal terms,
after applications of Fourier analysis methods.
