On the exact controllability of a Galerkin scheme for 3D viscoelastic fluids with fractional Laplacian viscosity and anisotropic filtering

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-11-03 DOI:10.1002/zamm.202300056
Luca Bisconti, Davide Catania
{"title":"On the exact controllability of a Galerkin scheme for 3D viscoelastic fluids with fractional Laplacian viscosity and anisotropic filtering","authors":"Luca Bisconti, Davide Catania","doi":"10.1002/zamm.202300056","DOIUrl":null,"url":null,"abstract":"Abstract We study a mathematical model describing 3D viscoelastic fluids with memory, fractional viscosity, and regularized by means of a horizontal anisotropic filter. This regularization is obtained through the action of the inverse of the horizontal Helmholtz operator, and the system is considered in a fully periodic space‐domain Ω. After introducing a controlled version of such a model, we take into account for it a suitable Galerkin approximation scheme. Exploiting the Hilbert uniqueness method, we establish the exact controllability of the finite‐dimensional Galerkin system.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"33 6","pages":"0"},"PeriodicalIF":2.3000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/zamm.202300056","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract We study a mathematical model describing 3D viscoelastic fluids with memory, fractional viscosity, and regularized by means of a horizontal anisotropic filter. This regularization is obtained through the action of the inverse of the horizontal Helmholtz operator, and the system is considered in a fully periodic space‐domain Ω. After introducing a controlled version of such a model, we take into account for it a suitable Galerkin approximation scheme. Exploiting the Hilbert uniqueness method, we establish the exact controllability of the finite‐dimensional Galerkin system.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
具有分数拉普拉斯黏度和各向异性滤波的三维粘弹性流体Galerkin格式的精确可控性
摘要研究了具有记忆、分数黏度、水平各向异性滤波器正则化的三维粘弹性流体的数学模型。这种正则化是通过水平亥姆霍兹算子的逆作用得到的,并且系统被认为是在一个全周期空间域Ω中。在引入这种模型的控制版本后,我们考虑了一个合适的伽辽金近似格式。利用希尔伯特唯一性方法,建立了有限维伽辽金系统的精确可控性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
期刊最新文献
A closed form solution for uniformly loaded rectangular plates with adjacent edges clamped and the two others simply supported (CCSS) Wave analysis in porous thermoelastic plate with microtemperature Transformational deformation models of continuous thin‐walled structural elements with support elements of finite sizes: Theoretical foundations, computational, and physical experiments On the exact controllability of a Galerkin scheme for 3D viscoelastic fluids with fractional Laplacian viscosity and anisotropic filtering An accurate and parameter‐free analysis for the converse Poynting effect in large constrained torsion of highly elastic soft tubes
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1