  We establish existence, uniqueness and stability of transonic shocks for
steady compressible non-isentropic potential flow system in a multidimensional
divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit
pressure. The proof is based on solving a free boundary problem for a system of
partial differential equations consisting of an elliptic equation and a
transport equation. In the process, we obtain unique solvability for a class of
transport equations with velocity fields of weak regularity(non-Lipschitz), an
infinite dimensional weak implicit mapping theorem which does not require
continuous Frechet differentiability, and regularity theory for a class of
elliptic partial differential equations with discontinuous oblique boundary
conditions.
