利用斯特克洛夫型和 Farwig 边界条件求解双谐波问题

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s1995080224602479

Giovanni Migliaccio, Hovik A. Matevossian

{"title":"利用斯特克洛夫型和 Farwig 边界条件求解双谐波问题","authors":"Giovanni Migliaccio, Hovik A. Matevossian","doi":"10.1134/s1995080224602479","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions\",\"authors\":\"Giovanni Migliaccio, Hovik A. Matevossian\",\"doi\":\"10.1134/s1995080224602479\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224602479\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602479","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要在本文中，我们考虑了一个双谐波问题，其边界的一部分具有 Steklov 型边界条件，另一部分具有 Farwig 条件。对于这个问题，研究了解的唯一性问题，在非唯一性情况下，只要加权 Dirichlet 积分是有界的，就可以确定所考虑问题的线性独立解的精确数目。利用变分原理，可以得到唯一性（非唯一性）定理，以及计算解空间维度的精确公式，这取决于加权狄利克特积分中包含的参数值。

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

Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions

Abstract

In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.

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

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.