Viscosity solutions to a Cauchy type problem for timelike Lorentzian eikonal equation
Analysis of PDEs
2023-10-13 v1 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2310.08058,
title = {Viscosity solutions to a Cauchy type problem for timelike Lorentzian eikonal equation},
author = {Siyao Zhu and Xiaojun Cui and Tianqi Shi},
journal= {arXiv preprint arXiv:2310.08058},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2309.15006