论文标题
混合类型的部分微分方程：分析和应用
Partial Differential Equations of Mixed Type: Analysis and Applications
论文作者
论文摘要
部分微分方程（PDE）是许多数学和科学进步的核心。尽管在过去八十年中，在标准类型的PDE理论方面取得了巨大进展，但对混合类型的非线性PDE的分析仍处于起步阶段。这份说明性论文的目的是通过几个长期存在的流体力学，差异几何形状和其他领域的基本问题来表明，在这些领域中产生的许多非线性PDE不再是标准类型，而是在PDES分类的边界，或者确实超出了分类超出分类的范围。还提供了一些相互关联的联系，历史观点，最新的发展以及当前的混合类型非线性PDE分析的趋势。
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of mixed type is still in its infancy. The aim of this expository paper is to show, through several longstanding fundamental problems in fluid mechanics, differential geometry, and other areas, that many nonlinear PDEs arising in these areas are no longer of standard types, but lie at the boundaries of the classification of PDEs or, indeed, go beyond the classification to be of mixed type. Some interrelated connections, historical perspectives, recent developments, and current trends in the analysis of nonlinear PDEs of mixed type are also presented.
