*主持人：袁海荣 教授

*讲座内容简介：
In this talk, the compressible non-isentropic Euler equations with combustion reaction are used as the model to study the stability of steady strong detonation waves in a two-dimensional straight duct with constant cross-section. We construct a special solution of strong detonation wave that only depends on the normal direction of the duct. The special solution is consistent with the flow field in the ideal sub-combustion ramjet, that is, there are supersonic and subsonic flows in the upstream and downstream of the strong detonation wave-front respectively, and automatic ignition can be realized through the detonation wave-front. We prove that almost all strong detonation waves are stable under the perturbations of the upstream supersonic flows and downstream back pressures satisfy some symmetry conditions. Mathematically, it is necessary to deal with the difficulties caused by the free boundary value problem of nonlocal strongly coupled elliptic-hyperbolic systems. Due to the strong coupling and interference between hyperbolic and elliptic modes in the steady subsonic Euler equations caused by combustion reaction, we construct a new method to solve this kind of problems by comprehensively applying functional analysis, harmonic analysis, analytical function, ordinary differential equation and linear algebra theory.

*主讲人简介：
高俊磊，2021年博士毕业于华东师范大学，现任浙江师范大学数学与计算机学院讲师，主要从事流体力学中偏微分方程的理论研究。