Work

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

Year: 2024

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0178336

Authors: Siyao Zhu, Xiaojun Cui, Tianqi Shi

Institution: Nanjing University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G3013816952