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Stabilization of a multi-dimensional system of hyperbolic balance laws 双曲平衡律多维系统的镇定
4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023033
Michael Herty, Ferdinand Thein
{"title":"Stabilization of a multi-dimensional system of hyperbolic balance laws","authors":"Michael Herty, Ferdinand Thein","doi":"10.3934/mcrf.2023033","DOIUrl":"https://doi.org/10.3934/mcrf.2023033","url":null,"abstract":"We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $ mathbb{R}^n $. A reformulation leads to a stabilization problem for a multi-dimensional system of $ n $ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $ L^2 $ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135551336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Dynamic programming principle for one kind of stochastic recursive optimal control problem with Markovian switching 一类具有马尔可夫切换的随机递归最优控制问题的动态规划原理
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023019
Li Guo, Zhen Wu
{"title":"Dynamic programming principle for one kind of stochastic recursive optimal control problem with Markovian switching","authors":"Li Guo, Zhen Wu","doi":"10.3934/mcrf.2023019","DOIUrl":"https://doi.org/10.3934/mcrf.2023019","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"70 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73531371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On stable solutions of the dynamical reconstruction and tracking control problems for a coupled ordinary differential equation–heat equation 常微分方程-热方程耦合动力学重构与跟踪控制问题的稳定解
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023005
V. Maksimov
{"title":"On stable solutions of the dynamical reconstruction and tracking control problems for a coupled ordinary differential equation–heat equation","authors":"V. Maksimov","doi":"10.3934/mcrf.2023005","DOIUrl":"https://doi.org/10.3934/mcrf.2023005","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88819321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global well-posedness for the fourth-order Hartree-type Schrödinger equation with Cauchy data in $ L^{p} $ L^{p} $中具有柯西数据的四阶hartree型Schrödinger方程的全局适定性
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023015
Jin Xie, Deng Wang, Han Yang
{"title":"Global well-posedness for the fourth-order Hartree-type Schrödinger equation with Cauchy data in $ L^{p} $","authors":"Jin Xie, Deng Wang, Han Yang","doi":"10.3934/mcrf.2023015","DOIUrl":"https://doi.org/10.3934/mcrf.2023015","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82441493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal distributed control for a Cahn-Hilliard type phase field system related to tumor growth 与肿瘤生长相关的Cahn-Hilliard型相场系统的最优分布控制
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023017
Bo You
{"title":"Optimal distributed control for a Cahn-Hilliard type phase field system related to tumor growth","authors":"Bo You","doi":"10.3934/mcrf.2023017","DOIUrl":"https://doi.org/10.3934/mcrf.2023017","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"30 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83381649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimality conditions for optimal control of non-well-posed p-Laplacian elliptic equations 非适定p-拉普拉斯椭圆方程最优控制的最优性条件
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023018
H. Lou, Shu Luan
{"title":"Optimality conditions for optimal control of non-well-posed p-Laplacian elliptic equations","authors":"H. Lou, Shu Luan","doi":"10.3934/mcrf.2023018","DOIUrl":"https://doi.org/10.3934/mcrf.2023018","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"120 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76689643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coefficient inverse problem for anisotropic time-domain wave equation 各向异性时域波动方程的系数反问题
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023006
Houssem Lihiou
{"title":"Coefficient inverse problem for anisotropic time-domain wave equation","authors":"Houssem Lihiou","doi":"10.3934/mcrf.2023006","DOIUrl":"https://doi.org/10.3934/mcrf.2023006","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78747363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A long-term optimal consumption and investment problem with partial information 具有部分信息的长期最优消费与投资问题
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023028
H. Hata
{"title":"A long-term optimal consumption and investment problem with partial information","authors":"H. Hata","doi":"10.3934/mcrf.2023028","DOIUrl":"https://doi.org/10.3934/mcrf.2023028","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"46 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78881149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Study approximate controllability and null controllability of neutral delay Hilfer fractional stochastic integrodifferential system with Rosenblatt process 研究了具有Rosenblatt过程的中性延迟Hilfer分数阶随机积分微分系统的近似可控性和零可控性
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023010
H. Ahmed
{"title":"Study approximate controllability and null controllability of neutral delay Hilfer fractional stochastic integrodifferential system with Rosenblatt process","authors":"H. Ahmed","doi":"10.3934/mcrf.2023010","DOIUrl":"https://doi.org/10.3934/mcrf.2023010","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"2 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75277076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Feedback stabilization of a parabolic coupled system and its numerical study 抛物型耦合系统的反馈镇定及其数值研究
4区 数学
Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2023022
Wasim Akram, Debanjana Mitra, Neela Nataraj, Mythily Ramaswamy
{"title":"Feedback stabilization of a parabolic coupled system and its numerical study","authors":"Wasim Akram, Debanjana Mitra, Neela Nataraj, Mythily Ramaswamy","doi":"10.3934/mcrf.2023022","DOIUrl":"https://doi.org/10.3934/mcrf.2023022","url":null,"abstract":"In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with exponential decay $ -omega<0 $ for any $ omega>0 $. A stabilizing control is found in feedback form by solving a suitable algebraic Riccati equation. In the second part, a conforming finite element method is employed to approximate the continuous system by a finite dimensional discrete system. The approximated system is also feedback stabilizable (uniformly) with exponential decay $ -omega+epsilon $, for any $ epsilon>0 $ and the feedback control is obtained by solving a discrete algebraic Riccati equation. The error estimate of stabilized solutions as well as stabilizing feedback controls are obtained. We validate the theoretical results by numerical implementations.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135828098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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