具有时型边界的全局双曲流形上friedrich系统的Cauchy问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-07-06 DOI:10.57262/ade027-0708-497

N. Ginoux, S. Murro

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引用次数: 14

摘要

研究了一类具有类时边界的全局双曲流形上的friedrich系统的Cauchy问题。通过施加容许边界条件，证明了强解的存在性和唯一性。进一步证明了如果Friedrichs系统是双曲的，柯西问题在Hadamard意义上是适定的。最后给出了具有容许边界条件的Friedrichs系统的实例。关键词:对称双曲系统，对称正系统，可容许边界条件，Dirac算子，通常双曲算子，Klein-Gordon算子，热算子，反应扩散算子，具有时间边界的全局双曲流形。

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On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.