  Transonic shocks play a pivotal role in designation of supersonic inlets and
ramjets. For the three-dimensional steady non-isentropic compressible Euler
system with frictions, we had constructed a family of transonic shock solutions
in rectilinear ducts with square cross-sections, and this paper is devoted to
proving rigorously that almost all of these transonic shock solutions are
stable, under multidimensional small perturbations of the upcoming supersonic
flows and back pressures at the exits of ducts in suitable function spaces.
This manifests that friction has a stabilization effect on transonic shocks in
ducts, in consideration of previous works have shown that transonic shocks in
purely steady Euler flows are not stable in such ducts. Except its implications
to applications, since frictions lead to a stronger coupling between the
elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler
system, we develop the framework established in previous works to study more
complex and interesting Venttsel problems of nonlocal elliptic equations.
