On the mean field games system with lateral Cauchy data via Carleman estimates

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2024-01-31 DOI:10.1515/jiip-2023-0089

Michael V. Klibanov, Jingzhi Li, Hongyu Liu

引用次数: 0

Abstract

The second-order mean field games system (MFGS) in a bounded domain with the lateral Cauchy data are considered. This means that both Dirichlet and Neumann boundary data for the solution of the MFGS are given. Two Hölder stability estimates for two slightly different cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral Cauchy data. Our stability estimates imply uniqueness. The key mathematical apparatus is the apparatus of two new Carleman estimates.

查看原文本刊更多论文

通过卡勒曼估计论有横向考奇数据的均值场博弈系统

研究考虑了有界域中的二阶均值场博弈系统（MFGS）与横向考奇数据。这意味着 MFGS 解的 Dirichlet 和 Neumann 边界数据均已给出。针对两种略有不同的情况，得出了两个霍尔德稳定性估计值。这些估计值表明了 MFGS 的解对于横向考奇数据中可能存在的噪声有多稳定。我们的稳定性估计值意味着唯一性。关键的数学工具是两个新的卡勒曼估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography