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 constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections. In this article, we are devoted to proving rigorously that a large class 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 frictions have a stabilization effect on transonic shocks in ducts, in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts. Except its implications to applications, because 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.

中文翻译：

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通过三维管道的稳态可压缩欧拉流中跨音速冲击的摩擦稳定效应

跨音速激波在指定超音速进气道和冲压发动机中起着关键作用。对于具有摩擦的三维稳态非等熵可压缩欧拉系统，我们在方形截面的直线管道中构造了一系列跨音速激波解。在本文中，我们致力于严格证明一大类跨音速激波解在即将到来的超音速流动的多维小扰动和合适的功能空间中管道出口处的背压下是稳定的。这表明摩擦对管道中的跨音速激波具有稳定作用，考虑到先前的工作表明，纯稳定欧拉流中的跨音速激波在此类管道中是不稳定的。除了对应用程序的影响，