{"title":"优化非局部控制问题的形状","authors":"Zhiwei Cheng, Hayk Mikayelyan","doi":"10.1007/s13540-024-00318-9","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimization of the shape for a non-local control problem\",\"authors\":\"Zhiwei Cheng, Hayk Mikayelyan\",\"doi\":\"10.1007/s13540-024-00318-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00318-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00318-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
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。
Optimization of the shape for a non-local control problem
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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