Determining Lorentzian manifold from non-linear wave observation at a single point

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-06-27 DOI:10.1016/j.jde.2025.113563

Medet Nursultanov , Lauri Oksanen , Leo Tzou

引用次数: 0

Abstract

We consider an inverse problem for a non-linear hyperbolic equation. We show that the conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.

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从单点非线性波观测中确定洛伦兹流形

考虑一类非线性双曲型方程的反问题。我们证明了洛伦兹流形的共形结构可以由沿单个类时曲线计算的源到解映射来确定。我们使用非线性波相互作用的微局部分析。

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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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics