跨音速流与混合型偏微分方程在瓦斯爆炸的防治技术和热力推进技术中有重要应用，但其数学理论相对滞后。因此，无论理论研究的需求、背景科学的需求还是培养青年学者的需求，都使得加强跨音速流与混合型偏微分方程的研讨变得非常迫切。基于此，我们申请举办跨音速流及混合型偏微分方程高级研讨班项目。本次研讨班旨在汇聚国内在这一领域进行了长期探讨并卓有成效的中青年专家，在著名的偏微分方程专家辛周平教授的带领下，以混合型、退化性偏微分方程和高维激波的形成为主攻领域，采用主讲、提问、研讨、合作撰写论文等灵活多样的形式开展研讨班。力争提出和解决一系列具有国际水准的数学理论问题。本次研讨班将努力探索一条适用的、有效的合作研究模式。厦门大学也有一支锐意进取的偏微分方程队伍，非常乐意提供条件优越的研讨场所，欢迎专家在空气清新、气候宜人的优美的校园环境中进行研讨。我们恳请专家能提供交流所需要的经费。

The transonic flow and mixed PDEs have imporant applications in control techniques of gas explosion and propulsion technology of engine, but their mathematical theory is still quite backward. Hence, the need of theoretical reseach, backgroud science and the cultivation of youth researchers, is essential to strengthen the research on mixed PDEs. Therefore, we apply to hold the advanced research seminar. The aim of the advanced seminar is to make young anf middle-aged exports who is exploring for a long time and achieved remarkable results in this field converge on a crucial team. The famous PDEs' expert, Prof. Zhouping Xin organize the advanced seminar. We make the mixed and degenerate PDEs and the formation of free interface as the main attack field, and adopt mutiple kinds of patterns to implement the seminar, such as giving lectures, asking questions, discussing and co-authoring papers. We try to put forward and work out a series of international level problems for mathematical theory, explore a kind of cooperative model for applicative and effective reseach. Xiamen University has an aggressive group in PDEs field, and is very pleased to provide space with good conditions to hold advanced seminar on PDEs, so that it will be a great success in such a beautiful campus with fresh air and comprehensive facilities. We hope that Tian Yuan Fund will provide financial support.