微波加热问题非局部表述的解存在定理

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2024-02-28 DOI:10.1007/s11565-024-00491-y

Giovanni Cimatti

{"title":"微波加热问题非局部表述的解存在定理","authors":"Giovanni Cimatti","doi":"10.1007/s11565-024-00491-y","DOIUrl":null,"url":null,"abstract":"<div><p>Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder’s fixed point theorem.\n</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 2","pages":"533 - 545"},"PeriodicalIF":0.0000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00491-y.pdf","citationCount":"0","resultStr":"{\"title\":\"A theorem of existence of solution for the nonlocal formulation of the problem of microwave heating\",\"authors\":\"Giovanni Cimatti\",\"doi\":\"10.1007/s11565-024-00491-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder’s fixed point theorem.\\n</p></div>\",\"PeriodicalId\":35009,\"journal\":{\"name\":\"Annali dell''Universita di Ferrara\",\"volume\":\"70 2\",\"pages\":\"533 - 545\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11565-024-00491-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali dell''Universita di Ferrara\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11565-024-00491-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-024-00491-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

微波电磁加热被广泛应用于许多工业流程中。所涉及的数学是基于麦克斯韦方程与热方程的耦合。热导率与温度密切相关，而温度本身又是 P.D.E 系统的一个未知数。我们在此提出一个模型，利用非局部项作为加热源来简化这种耦合。我们利用 Schauder 定点定理证明了相应的数学初界值问题有解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A theorem of existence of solution for the nonlocal formulation of the problem of microwave heating

Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder’s fixed point theorem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.