一阶项和零阶项耦合随机抛物方程的零可控性

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-02-12 DOI:10.1007/s00245-025-10231-z

Mahmoud Baroun, Said Boulite, Abdellatif Elgrou, Lahcen Maniar

{"title":"一阶项和零阶项耦合随机抛物方程的零可控性","authors":"Mahmoud Baroun, Said Boulite, Abdellatif Elgrou, Lahcen Maniar","doi":"10.1007/s00245-025-10231-z","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the null controllability of forward and backward linear stochastic parabolic equations with first and zero order coupling terms, and with bounded coefficients. The null controllability results rely on novel Carleman estimates for the backward and forward adjoint equations, established through the application of the duality technique. In doing so, we resolve an open question (see Remark 2.2 in [Tang and Zhang in SIAM J Control Optim 48:2191–2216, 2009]). Moreover, we provide more accurate estimates for the null-control costs.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Null Controllability for Stochastic Parabolic Equations Coupled by First and Zero Order Terms\",\"authors\":\"Mahmoud Baroun, Said Boulite, Abdellatif Elgrou, Lahcen Maniar\",\"doi\":\"10.1007/s00245-025-10231-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the null controllability of forward and backward linear stochastic parabolic equations with first and zero order coupling terms, and with bounded coefficients. The null controllability results rely on novel Carleman estimates for the backward and forward adjoint equations, established through the application of the duality technique. In doing so, we resolve an open question (see Remark 2.2 in [Tang and Zhang in SIAM J Control Optim 48:2191–2216, 2009]). Moreover, we provide more accurate estimates for the null-control costs.</p></div>\",\"PeriodicalId\":55566,\"journal\":{\"name\":\"Applied Mathematics and Optimization\",\"volume\":\"91 2\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00245-025-10231-z\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10231-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

证明了具有一阶和零阶耦合项和有界系数的正反向线性随机抛物方程的零可控性。零可控性结果依赖于通过对偶技术建立的后向和正向伴随方程的新颖Carleman估计。通过这样做，我们解决了一个悬而未决的问题（见[Tang and Zhang] In SIAM J Control Optim 48:21 191 - 2216,2009]中的注释2.2）。此外，我们对零控制成本提供了更准确的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Null Controllability for Stochastic Parabolic Equations Coupled by First and Zero Order Terms

We prove the null controllability of forward and backward linear stochastic parabolic equations with first and zero order coupling terms, and with bounded coefficients. The null controllability results rely on novel Carleman estimates for the backward and forward adjoint equations, established through the application of the duality technique. In doing so, we resolve an open question (see Remark 2.2 in [Tang and Zhang in SIAM J Control Optim 48:2191–2216, 2009]). Moreover, we provide more accurate estimates for the null-control costs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.