{"title":"Bitsadze–Samarsky Type Nonlocal Boundary Value Problem for a Second Kind Mixed Equation with a Conjugation Condition of the Frankl Type","authors":"B. I. Islomov, A. A. Abdullayev","doi":"10.1134/s1995080224600626","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","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/s1995080224600626","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.
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.
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