论文标题
关于弗里德里奇系统在全球双曲线歧管上的凯奇问题上
On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary
论文作者
论文摘要
在本文中，研究了弗里德里奇系统在全球双曲线歧管上的凯奇问题，并研究了及时的边界。通过施加可接受的边界条件，显示了强溶液的存在和独特性。此外，如果弗里德里希（Friedrichs）系统是双曲的，则证明凯奇（Cauchy）的问题在哈玛德（Hadamard）的意义上被证明是良好的。最后，提供了具有可接受边界条件的弗里德里奇系统的示例。关键字：对称双曲系统，对称正面系统，可接受的边界条件，狄拉克运算符，通常是双曲线操作员，klein-gordon操作员，热运算符，热操作员，反应 - 扩散操作员，具有时间表边界的全球双曲线歧管。
In this paper, the Cauchy problem for a Friedrichs system on a globally hyperbolic manifold with a timelike boundary is investigated. By imposing admissible boundary conditions, the existence and the uniqueness of strong solutions are shown. Furthermore, if the Friedrichs system is hyperbolic, the Cauchy problem is proved to be well-posed in the sense of Hadamard. Finally, examples of Friedrichs systems with admissible boundary conditions are provided. Keywords: symmetric hyperbolic systems, symmetric positive systems, admissible boundary conditions, Dirac operator, normally hyperbolic operator, Klein-Gordon operator, heat operator, reaction-diffusion operator, globally hyperbolic manifolds with timelike boundary.
