{"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":null,"pages":null},"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.
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.