有质量源的Cahn–Hilliard方程的双曲松弛

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Asymptotic Analysis Pub Date : 2023-06-14 DOI:10.3233/asy-231844

Dieunel Dor

{"title":"有质量源的Cahn–Hilliard方程的双曲松弛","authors":"Dieunel Dor","doi":"10.3233/asy-231844","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the hyperbolic Cahn–Hilliard equation with a proliferation term, which has applications in biology. First, we study the well-posedness and the regularity of the solutions, which then allow us to study the dissipativity and the high-order dissipativity and finally the existence of the exponential attractor with Dirichlet boundary conditions. Finally, we give numerical simulations that confirm the results.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the hyperbolic relaxation of the Cahn–Hilliard equation with a mass source\",\"authors\":\"Dieunel Dor\",\"doi\":\"10.3233/asy-231844\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider the hyperbolic Cahn–Hilliard equation with a proliferation term, which has applications in biology. First, we study the well-posedness and the regularity of the solutions, which then allow us to study the dissipativity and the high-order dissipativity and finally the existence of the exponential attractor with Dirichlet boundary conditions. Finally, we give numerical simulations that confirm the results.\",\"PeriodicalId\":55438,\"journal\":{\"name\":\"Asymptotic Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asymptotic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3233/asy-231844\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-231844","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

在本文中，我们考虑了具有增殖项的双曲型Cahn–Hilliard方程，该方程在生物学中有应用。首先，我们研究了解的适定性和正则性，这使我们能够研究耗散性和高阶耗散性，最后研究具有Dirichlet边界条件的指数吸引子的存在性。最后，我们进行了数值模拟，验证了结果。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On the hyperbolic relaxation of the Cahn–Hilliard equation with a mass source

In this paper, we consider the hyperbolic Cahn–Hilliard equation with a proliferation term, which has applications in biology. First, we study the well-posedness and the regularity of the solutions, which then allow us to study the dissipativity and the high-order dissipativity and finally the existence of the exponential attractor with Dirichlet boundary conditions. Finally, we give numerical simulations that confirm the results.

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

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.