INVERSE PROBLEMS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: SOME PROGRESSES AND OPEN PROBLEMS

被引：6

作者：

Lu, Qi ^{[1
]}

Zhang, Xu ^{[1
,2
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu, Peoples R China

[2] Sichuan Univ, New Cornerstone Sci Lab, Chengdu, Peoples R China

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2024年 / 14卷 / 02期

关键词：

Inverse problem; Carleman estimate; stochastic hyperbolic equation; stochasitic parabolic equation; UNIQUE CONTINUATION; OBSERVABILITY ESTIMATE; CARLEMAN;

D O I：

10.3934/naco.2023014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to survey some recent works on inverse problems for stochastic partial differential equations (SPDEs for short), which were solved by means of Carleman estimate. For simplicity, we focus on two typical SPDEs, i.e, stochastic hyperbolic equations and stochastic parabolic equations. Our particular concerns are those inverse problems which are genuinely stochastic and therefore cannot be reduced to any deterministic ones. Also, some open problems are presented.

引用

页码：227 / 272

页数：46

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