双调和热方程解的局部一致收敛性和最终正性

IF 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations Pub Date : 2021-11-04 DOI:10.57262/die036-0910-727

D. Daners, Jochen Gluck, J. Mui

{"title":"双调和热方程解的局部一致收敛性和最终正性","authors":"D. Daners, Jochen Gluck, J. Mui","doi":"10.57262/die036-0910-727","DOIUrl":null,"url":null,"abstract":"We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Local uniform convergence and eventual positivity of solutions to biharmonic heat equations\",\"authors\":\"D. Daners, Jochen Gluck, J. Mui\",\"doi\":\"10.57262/die036-0910-727\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.\",\"PeriodicalId\":50581,\"journal\":{\"name\":\"Differential and Integral Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential and Integral Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/die036-0910-727\",\"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":"Differential and Integral Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/die036-0910-727","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: 4

摘要

在Dirichlet边界条件下，我们研究了具有有界光滑截面的无限圆柱体上与双调和算子相关的演化方程。重点是大时间解的渐近性和正性。特别是，我们得出了解决方案的局部最终积极性。进一步证明了双调和热方程解的局部最终正性及其在欧氏空间上的推广。我们分析的主要工具是傅立叶变换和光谱方法。

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

Local uniform convergence and eventual positivity of solutions to biharmonic heat equations

We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.

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

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.