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Optimal control for a free boundary tumor growth model 自由边界肿瘤生长模型的最优控制
4区 数学
Evolution Equations and Control Theory Pub Date : 2025-01-01 DOI: 10.3934/eect.2025043
Yixiang Wu, Xinyue Evelyn Zhao, Rachel Leander, Wandi Ding
{"title":"Optimal control for a free boundary tumor growth model","authors":"Yixiang Wu, Xinyue Evelyn Zhao, Rachel Leander, Wandi Ding","doi":"10.3934/eect.2025043","DOIUrl":"https://doi.org/10.3934/eect.2025043","url":null,"abstract":"This paper investigates the optimal control of treatment in a free boundary PDE model that describes the growth of a radially symmetric tumor. The optimal control strategy is designed to inhibit tumor growth while minimizing side effects. We establish the well-posedness of the problem and prove the existence of an optimal control. In order to characterize this optimal control, the optimality system is derived, and a necessary condition is obtained. Numerical simulations are conducted to illustrate our theoretical findings and assess the impact of the optimal control strategy on tumor growth dynamics. Furthermore, we extend the model to include spatial dependency in the control variable and perform additional simulations to explore this more complex scenario.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"14 6","pages":"1534-1564"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.aimsciences.org/data/article/export-pdf?id=6846b27db924fa00d9d4bb9e","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147382154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local null controllability of a class of non-Newtonian incompressible viscous fluids 一类非牛顿不可压缩粘性流体的局部零可控性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-07-09 DOI: 10.3934/eect.2021043
P. P. Carvalho, J. Límaco, Denilson Menezes, Yuri Thamsten
{"title":"Local null controllability of a class of non-Newtonian incompressible viscous fluids","authors":"P. P. Carvalho, J. Límaco, Denilson Menezes, Yuri Thamsten","doi":"10.3934/eect.2021043","DOIUrl":"https://doi.org/10.3934/eect.2021043","url":null,"abstract":"We investigate the null controllability property of systems that mathematically describe the dynamics of some non-Newtonian incompressible viscous flows. The principal model we study was proposed by O. A. Ladyzhenskaya, although the techniques we develop here apply to other fluids having a shear-dependent viscosity. Taking advantage of the Pontryagin Minimum Principle, we utilize a bootstrapping argument to prove that sufficiently smooth controls to the forced linearized Stokes problem exist, as long as the initial data in turn has enough regularity. From there, we extend the result to the nonlinear problem. As a byproduct, we devise a quasi-Newton algorithm to compute the states and a control, which we prove to converge in an appropriate sense. We finish the work with some numerical experiments.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"22 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73081150","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: 1
A Newtonian approach to general black holes 用牛顿理论研究一般黑洞
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-03-24 DOI: 10.3934/eect.2023019
A. Haraux
{"title":"A Newtonian approach to general black holes","authors":"A. Haraux","doi":"10.3934/eect.2023019","DOIUrl":"https://doi.org/10.3934/eect.2023019","url":null,"abstract":"We show how it is possible to define and study black holes of arbitrary shapes in the framework of Newtonian mechanics.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"58 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74963150","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
Riccati-based solution to the optimal control of linear evolution equations with finite memory 有限记忆线性演化方程最优控制的riccati解
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-03-09 DOI: 10.3934/eect.2023035
P. Acquistapace, F. Bucci
{"title":"Riccati-based solution to the optimal control of linear evolution equations with finite memory","authors":"P. Acquistapace, F. Bucci","doi":"10.3934/eect.2023035","DOIUrl":"https://doi.org/10.3934/eect.2023035","url":null,"abstract":"In this article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution, following the variational approach utilized in the study of the linear-quadratic problem for memoryless infinite dimensional systems, we attain a closed-loop form of the unique optimal control via certain operators that are shown to solve a coupled system of quadratic differential equations. This result provides a first extension to the partial differential equations realm of the Riccati-based theory recently devised by L. Pandolfi in a finite dimensional context.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"88 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75709347","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 the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime de Sitter时空中Hartree型半线性Schrödinger方程的Cauchy问题
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023028
Mikio Ichimiya, M. Nakamura
{"title":"On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime","authors":"Mikio Ichimiya, M. Nakamura","doi":"10.3934/eect.2023028","DOIUrl":"https://doi.org/10.3934/eect.2023028","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"125 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91135163","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
Singular limits and dynamics for the abstract Timoshenko system 抽象Timoshenko系统的奇异极限和动力学
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023037
M. Freitas, M. J. Santos, Dilberto S. Almeida Jr., Mauro L. Santos, A. Ramos
{"title":"Singular limits and dynamics for the abstract Timoshenko system","authors":"M. Freitas, M. J. Santos, Dilberto S. Almeida Jr., Mauro L. Santos, A. Ramos","doi":"10.3934/eect.2023037","DOIUrl":"https://doi.org/10.3934/eect.2023037","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"19 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87714510","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
Cone-bounded feedback laws for linear second order systems 线性二阶系统的锥有界反馈律
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023006
Abdellaziz Binid, A. M. Taboye, M. Laabissi
{"title":"Cone-bounded feedback laws for linear second order systems","authors":"Abdellaziz Binid, A. M. Taboye, M. Laabissi","doi":"10.3934/eect.2023006","DOIUrl":"https://doi.org/10.3934/eect.2023006","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"30 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89767637","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
Stabilization of an interconnected system of Schrödinger and wave equations with boundary coupling 具有边界耦合的Schrödinger与波动方程互联系统的镇定
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023022
Latifa Moumen, Fatima Zohra Sidiali, S. Rebiai
{"title":"Stabilization of an interconnected system of Schrödinger and wave equations with boundary coupling","authors":"Latifa Moumen, Fatima Zohra Sidiali, S. Rebiai","doi":"10.3934/eect.2023022","DOIUrl":"https://doi.org/10.3934/eect.2023022","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"39 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80221486","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
Hyers-Ulam stability result for Hilfer fractional integrodifferential stochastic equations with fractional noises and non-instantaneous impulses 具有分数阶噪声和非瞬时脉冲的Hilfer分数阶积分微分随机方程的Hyers-Ulam稳定性结果
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023042
J. Priyadharsini, P. Balasubramaniam
{"title":"Hyers-Ulam stability result for Hilfer fractional integrodifferential stochastic equations with fractional noises and non-instantaneous impulses","authors":"J. Priyadharsini, P. Balasubramaniam","doi":"10.3934/eect.2023042","DOIUrl":"https://doi.org/10.3934/eect.2023042","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"102 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79392079","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
Approximation of mild solutions of delay integro-differential equations on Banach spaces Banach空间上时滞积分微分方程温和解的逼近
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI: 10.3934/eect.2023029
Mohammed Elghandouri, K. Ezzinbi
{"title":"Approximation of mild solutions of delay integro-differential equations on Banach spaces","authors":"Mohammed Elghandouri, K. Ezzinbi","doi":"10.3934/eect.2023029","DOIUrl":"https://doi.org/10.3934/eect.2023029","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"31 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79621803","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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