二维域中与抛物线-椭圆化合推进系统相关的优化控制问题

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-05-20 DOI:10.1007/s00245-024-10120-x

Jinxia Cen, Julio Huayta-Centeno, Exequiel Mallea-Zepeda, Shengda Zeng

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引用次数: 0

摘要

在本文中，我们研究了一个与二维域中带有线性生产项的抛物线-椭圆形化学推进系统相关的最优控制问题。在控制子域 \(\varOmega _c\) 上注入/提取化学物质的条件下，我们证明了全局时间强解的存在性和唯一性。之后，对于最优控制问题，我们证明了至少一个全局最优解的存在，并通过拉格朗日乘数定理推导出最优系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An Optimal Control Problem Related to a Parabolic–Elliptic Chemo-repulsion System in 2D Domains

In this paper we study an optimal control problem associated to a parabolic–elliptic chemo-repulsion system with a linear production term in a two-dimensional domain. Under the injection/extract chemical substance on a control subdomain \(\varOmega _c\), we prove the existence and uniqueness of global-in-time strong solutions. Afterwards, for the optimal control problem, we prove the existence of at least one global optimal solution, and derive an optimality system via using a Lagrange multipliers theorem.

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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.