Optimization of the shape for a non-local control problem

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-08-07 DOI:10.1007/s13540-024-00318-9

Zhiwei Cheng, Hayk Mikayelyan

引用次数: 0

Abstract

The paper studies the fractional order version of the reinforced membrane problem introduced in [A. Henrot and H. Maillot, 2001]. Existence and uniqueness of the solutions of the corresponding non-local equations has been proven for the relaxed problem. In addition, for the radial symmetric case the existence of the optimal domain has been shown.

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优化非局部控制问题的形状

本文研究了[A. Henrot 和 H. Maillot, 2001]中提出的分数阶强化膜问题。对于松弛问题，证明了相应非局部方程解的存在性和唯一性。此外，还证明了径向对称情况下最优域的存在性。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.