Stability of transonic shocks for the full Euler system in supersonic flow past a wedge

We study the stability of transonic shocks in steady supersonic flow past a wedge. It is known that in generic case such a problem admits two possible locations of the shock front, connecting the flow ahead of it and behind it. They can be distinguished as supersonic-supersonic shock and supersonic-subsonic shock (or transonic shock). Both these possible shocks satisfy the RankineHugoniot conditions and the entropy condition. We prove that the transonic shock is conditionally stable under perturbation of the upstream flow or perturbation of wedge boundary.