具有记忆的粘弹性连续体非齐次动力问题的弱可解性

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-09-05 DOI:10.1134/S0016266323010082

V. G. Zvyagin, V. P. Orlov

{"title":"具有记忆的粘弹性连续体非齐次动力问题的弱可解性","authors":"V. G. Zvyagin, V. P. Orlov","doi":"10.1134/S0016266323010082","DOIUrl":null,"url":null,"abstract":"<p> The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"74 - 79"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Weak Solvability of an Inhomogeneous Dynamic Problem for a Viscoelastic Continuum with Memory\",\"authors\":\"V. G. Zvyagin, V. P. Orlov\",\"doi\":\"10.1134/S0016266323010082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used. </p>\",\"PeriodicalId\":575,\"journal\":{\"name\":\"Functional Analysis and Its Applications\",\"volume\":\"57 1\",\"pages\":\"74 - 79\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Functional Analysis and Its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016266323010082\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266323010082","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

证明了具有记忆的粘弹性流体沿非光滑速度场非齐次边界条件运动方程初边值问题弱解的存在性。分析涉及到原始问题的伽辽金型近似，然后通过基于先验估计的极限。为了研究非光滑速度场的轨迹行为，应用了正则拉格朗日流动理论。

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

The Weak Solvability of an Inhomogeneous Dynamic Problem for a Viscoelastic Continuum with Memory

The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used.

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

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.