描述肿瘤生长的logistic源粘性Cahn-Hilliard-Keller-Segel模型的营养控制

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-09-16 DOI:10.3934/dcdss.2023123

G. Gilardi, A. Signori, J. Sprekels

{"title":"描述肿瘤生长的logistic源粘性Cahn-Hilliard-Keller-Segel模型的营养控制","authors":"G. Gilardi, A. Signori, J. Sprekels","doi":"10.3934/dcdss.2023123","DOIUrl":null,"url":null,"abstract":"In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution is obtained as a nontrivial combination of a Cahn-Hilliard type system accounting for the segregation between tumor cells and healthy cells, with a Keller-Segel type equation accounting for the evolution of a nutrient species and modeling the chemotaxis phenomenon. First, we develop a robust mathematical background that allows us to analyze an associated optimal control problem. This analysis forced us to select a source term of logistic type in the nutrient equation and to restrict the analysis to the case of two space dimensions. Then, the existence of an optimal control and first-order necessary conditions for optimality are established.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Nutrient control for a viscous Cahn–Hilliard–Keller–Segel model with logistic source describing tumor growth\",\"authors\":\"G. Gilardi, A. Signori, J. Sprekels\",\"doi\":\"10.3934/dcdss.2023123\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution is obtained as a nontrivial combination of a Cahn-Hilliard type system accounting for the segregation between tumor cells and healthy cells, with a Keller-Segel type equation accounting for the evolution of a nutrient species and modeling the chemotaxis phenomenon. First, we develop a robust mathematical background that allows us to analyze an associated optimal control problem. This analysis forced us to select a source term of logistic type in the nutrient equation and to restrict the analysis to the case of two space dimensions. Then, the existence of an optimal control and first-order necessary conditions for optimality are established.\",\"PeriodicalId\":48838,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems-Series S\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems-Series S\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/dcdss.2023123\",\"RegionNum\":4,\"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":"Discrete and Continuous Dynamical Systems-Series S","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcdss.2023123","RegionNum":4,"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: 1

摘要

在本文中，我们解决了一个描述肿瘤进化的偏微分方程系统的分布式控制问题，该系统考虑了趋化性的生物学机制。描述进化的系统是由Cahn-Hilliard型系统(用于解释肿瘤细胞和健康细胞之间的分离)和Keller-Segel型方程(用于解释营养物质的进化并模拟趋化现象)组成的一个重要组合。首先，我们开发了一个强大的数学背景，使我们能够分析相关的最优控制问题。这种分析迫使我们在营养方程中选择一个逻辑型源项，并将分析限制在两个空间维度的情况下。然后，建立了最优控制的存在性和最优性的一阶必要条件。

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

Nutrient control for a viscous Cahn–Hilliard–Keller–Segel model with logistic source describing tumor growth

In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution is obtained as a nontrivial combination of a Cahn-Hilliard type system accounting for the segregation between tumor cells and healthy cells, with a Keller-Segel type equation accounting for the evolution of a nutrient species and modeling the chemotaxis phenomenon. First, we develop a robust mathematical background that allows us to analyze an associated optimal control problem. This analysis forced us to select a source term of logistic type in the nutrient equation and to restrict the analysis to the case of two space dimensions. Then, the existence of an optimal control and first-order necessary conditions for optimality are established.

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

Discrete and Continuous Dynamical Systems-Series S MATHEMATICS, APPLIED-

CiteScore

3.70

自引率

5.60%

发文量

177

期刊介绍： Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.