带正则化项的Cahn-Hilliard方程

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2023-01-03 DOI:10.3233/asy-221821

Rim Mheich

{"title":"带正则化项的Cahn-Hilliard方程","authors":"Rim Mheich","doi":"10.3233/asy-221821","DOIUrl":null,"url":null,"abstract":"We will study in this article the nonlinear Cahn–Hilliard equation with proliferation and regularization terms with regular and logarithmic potentials. First, we consider the regular potential case, we show that the solutions blow up in finite time or exist globally in time. Furthermore, we prove that the model possess a global attractor. In addition, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. In the second part, we consider the logarithmic potential case and show the existence of a global solution.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cahn–Hilliard equation with regularization term\",\"authors\":\"Rim Mheich\",\"doi\":\"10.3233/asy-221821\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We will study in this article the nonlinear Cahn–Hilliard equation with proliferation and regularization terms with regular and logarithmic potentials. First, we consider the regular potential case, we show that the solutions blow up in finite time or exist globally in time. Furthermore, we prove that the model possess a global attractor. In addition, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. In the second part, we consider the logarithmic potential case and show the existence of a global solution.\",\"PeriodicalId\":55438,\"journal\":{\"name\":\"Asymptotic Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asymptotic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3233/asy-221821\",\"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-221821","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: 0

摘要

本文将研究具有正则势和对数势的扩散项和正则项的非线性Cahn-Hilliard方程。首先，我们考虑正则势情况，证明了解在有限时间内爆炸或在时间内全局存在。进一步证明了该模型具有全局吸引子。此外，我们构造了一类鲁棒的指数吸引子，即对扰动参数连续的吸引子。在第二部分，我们考虑对数势情况，并证明了全局解的存在性。

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

Cahn–Hilliard equation with regularization term

We will study in this article the nonlinear Cahn–Hilliard equation with proliferation and regularization terms with regular and logarithmic potentials. First, we consider the regular potential case, we show that the solutions blow up in finite time or exist globally in time. Furthermore, we prove that the model possess a global attractor. In addition, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. In the second part, we consider the logarithmic potential case and show the existence of a global solution.

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.