时间类洛伦兹埃克纳方程的考奇类问题的粘度解

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-09-10 DOI:10.1063/5.0178336

Siyao Zhu, Xiaojun Cui, Tianqi Shi

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引用次数: 0

摘要

在本文中，我们针对全局双曲时空中的时间类洛伦兹伊科纳方程提出了一个考奇类型问题。对于该方程，由于已知 Cauchy 曲面上的解值，我们证明了 Cauchy 曲面过去集（未来集）上粘性解的存在。此外，当粘滞解的时间方向一致时，我们还得到了粘滞解的唯一性和稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Viscosity solutions to a Cauchy type problem for timelike Lorentzian eikonal equation

In this paper, we propose a Cauchy type problem to the timelike Lorentzian eikonal equation on a globally hyperbolic space-time. For this equation, as the value of the solution on a Cauchy surface is known, we prove the existence of viscosity solutions on the past set (future set) of the Cauchy surface. Furthermore, when the time orientation of viscosity solution is consistent, the uniqueness and stability of viscosity solutions are also obtained.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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