微波加热问题解的存在性及稳定性和不稳定性的Liapunoff判据

IF 1.1 4区数学 Q1 MATHEMATICS

Ricerche di Matematica Pub Date : 2023-11-26 DOI:10.1007/s11587-023-00825-6

Giovanni Cimatti

{"title":"微波加热问题解的存在性及稳定性和不稳定性的Liapunoff判据","authors":"Giovanni Cimatti","doi":"10.1007/s11587-023-00825-6","DOIUrl":null,"url":null,"abstract":"<p>The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"62 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of solutions for the problem of microwave heating and a Liapunoff criteria for stability and instability\",\"authors\":\"Giovanni Cimatti\",\"doi\":\"10.1007/s11587-023-00825-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.</p>\",\"PeriodicalId\":21373,\"journal\":{\"name\":\"Ricerche di Matematica\",\"volume\":\"62 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ricerche di Matematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11587-023-00825-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ricerche di Matematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11587-023-00825-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

应用伽辽金方法证明了材料电磁加热非线性偏微分方程组初边值问题至少有一个解的存在性。此外，还提出了基于李雅普诺夫函数的稳定性和不稳定性判据。

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

Existence of solutions for the problem of microwave heating and a Liapunoff criteria for stability and instability

The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.

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

Ricerche di Matematica Mathematics-Applied Mathematics

CiteScore

3.00

自引率

8.30%

发文量

期刊介绍： “Ricerche di Matematica” publishes high-quality research articles in any field of pure and applied mathematics. Articles must be original and written in English. Details about article submission can be found online.