一类双面退化聚集方程的最优控制

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2023-06-04 DOI:10.15388/namc.2023.28.32395

M. Bendahmane, Fahd Karami, Elmahdi Erraji, Abdelghafour Atlas, L. Afraites

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引用次数: 0

摘要

本文研究了一类非局部退化聚集模型的最优控制问题的数学分析。该模型描述了生物的聚集，如行人运动、趋化性、动物群。利用辅助非退化聚集方程、Faedo-Galerkin法(求解存在性结果)和对偶法(求解唯一性结果)建立了直接问题弱解的适定性(存在唯一性)。此外，对于伴随问题，我们证明了最小值的存在性和一阶必要条件。这项工作的主要新颖之处在于对我们的非局部退化聚集模型的控制。我们的结果与一些数值模拟相辅相成。

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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Optimal control for a two-sidedly degenerate aggregation equation

In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming. We establish the wellposedness (existence and uniqueness) for the weak solution of the direct problem by means of an auxiliary nondegenerate aggregation equation, the Faedo–Galerkin method (for the existence result) and duality method (for the uniqueness). Moreover, for the adjoint problem, we prove the existence result of minimizers and first-order necessary conditions. The main novelty of this work concerns the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.