异质多孔介质中最优控制问题解的存在性

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS IMA Journal of Mathematical Control and Information Pub Date : 2024-04-08 DOI:10.1093/imamci/dnae011

A Kundu, H S Mahato

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引用次数: 0

摘要

本文探讨了有关多孔介质中传输过程的优化控制问题。传输现象受扩散-反应方程支配，基本上是一个半线性抛物线系统。引入了一个 $L^{2}$ 成本（能量）函数，并在介质的多孔部分应用了控制（分布式）。主要目的是确定给定控制是否为最优控制，并分析最优控制与临界状态之间的关系。分析从受控系统的微观描述开始，然后通过周期均质化对系统进行放大。

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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Existence of solution for an optimal control problem in a heterogeneous porous medium

The paper explores an optimal control problem concerning transport processes in a porous medium. The transport phenomena is governed by diffusion-reaction equations, which is basically a semi-linear parabolic system. An $L^{2}$-cost (energy) functional is introduced, and control (distributed) is applied in the porous part of the medium. The primary objective is to characterize a given control to be an optimal control and analyse the relationship between optimal control and the adjoint state. The analysis commences with the microscopic description of the controlled system followed by upscaling the system via periodic homogenization.

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来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences. All submitted papers will be judged on their merits by at least two referees and a full paper report will be available to the intending authors. Submitted articles will in general be published in an issue within six months of submission. Papers should not have previously published, nor should they be undes consideration for publication in another journal. This Journal takes publication ethics very seriously. If misconduct is found or suspected after the manuscript is published, the journal will investigate the matter and this may result in the article subsequently being retracted.