AI 中文总结
本文针对扩张喷管中准一维全可压缩欧拉方程的时间周期强跨音速激波解，揭示其耗散机制并结合分数步线性化迭代法完成$C^1$存在性与动力学稳定性的证明。
AI 中文摘要
本文研究扩张喷管中准一维全可压缩欧拉方程含强跨音速激波的时间周期解的$C^1$存在性与动力学稳定性。我们揭示了兰金-于戈尼奥条件中隐藏的强跨音速激波的物理结构耗散机制，这使我们能够估计亚音速下游区域左声波在激波边界处引发的共振，借助该耗散，我们通过构造分数步线性化迭代方法完成了证明。
英文摘要
This paper studies the $C^1$ existence and dynamical stability of temporal periodic solutions involving strong transonic shocks for the quasi--one--dimensional full compressible Euler equations in diverging nozzles. We reveal the physical structural dissipation mechanism of strong transonic shocks hidden in the Rankine--Hugoniot conditions. This allows us to estimate the resonance at the shock boundary caused by the left acoustic waves in the subsonic downstream region. With this dissipation, we complete the proof by developing a fraction--step linearized iterative method.
