粘性正反向扩散方程中的移动相界面

IF 1.4 4区 数学 Q1 MATHEMATICS
Carina Geldhauser, Michael Herrmann, Dirk Janßen
{"title":"粘性正反向扩散方程中的移动相界面","authors":"Carina Geldhauser, Michael Herrmann, Dirk Janßen","doi":"10.1007/s10884-024-10382-7","DOIUrl":null,"url":null,"abstract":"<p>The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.\n</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"24 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations\",\"authors\":\"Carina Geldhauser, Michael Herrmann, Dirk Janßen\",\"doi\":\"10.1007/s10884-024-10382-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.\\n</p>\",\"PeriodicalId\":15624,\"journal\":{\"name\":\"Journal of Dynamics and Differential Equations\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10884-024-10382-7\",\"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":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-024-10382-7","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

具有双稳态非线性的困难扩散方程的粘性正则化预示了动态相变的滞后行为,但对其错综复杂的多尺度演化仍缺乏完整的数学理解。我们通过仔细研究特殊情况下的行波解,揭示了传播相界的精细结构。假定存在三线性构成关系,我们将描述所有具有单调轮廓的波,并通过一个正宽度的单界面连接两个相。我们进一步研究了与粘度消失或双线性极限相关的两种尖锐界面状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations

Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations

The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.

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
CiteScore
3.30
自引率
7.70%
发文量
116
审稿时长
>12 weeks
期刊介绍: Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信