{"title":"Construction of Fundamental Solution for an Odd-Order Equation","authors":"B. Yu. Irgashev","doi":"10.1134/s1063454123040180","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of an odd-order equation with multiple characteristics in a rectangular domain as the sum of these particular solutions. We show that the FS is a solution to an inhomogeneous equation with multiple characteristics in a rectangular domain. In turn, knowledge of FS allows us to construct a potential theory for its further use in solving boundary-value problems.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"125 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454123040180","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of an odd-order equation with multiple characteristics in a rectangular domain as the sum of these particular solutions. We show that the FS is a solution to an inhomogeneous equation with multiple characteristics in a rectangular domain. In turn, knowledge of FS allows us to construct a potential theory for its further use in solving boundary-value problems.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
