A Stationary Chemo-repulsion System with Nonlinear Production and a Bilinear Optimal Control Problem Related

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-09-13 DOI:10.1007/s00245-025-10323-w

Yankis R. Linares, Exequiel Mallea-Zepeda, Israel Villarreal-Tintaya

引用次数: 0

Abstract

In this paper we study a bilinear optimal control problem related to a 2D chemo-repulsion stationary model with nonlinear production term. Firstly, we prove the existence of strong solutions for each control given; then, for the extremal problem, we prove the existence of at least one global optimal solution. Afterwards, using a generic result on the existence of Lagrange multipliers, we obtain the so-called first-order necessary optimality conditions for local optimal solutions. Furthermore, we discuss an extension of the results to 3D domains.

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一类具有非线性生产的稳态化学排斥系统及双线性最优控制问题

本文研究了一类具有非线性生产项的二维化学排斥平稳模型的双线性最优控制问题。首先证明了给定控制的强解的存在性；然后，对于极值问题，我们证明了至少存在一个全局最优解。然后，利用拉格朗日乘子存在性的一般结果，得到了局部最优解的一阶必要最优性条件。此外，我们还讨论了将结果推广到三维域的问题。

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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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.