带有弗兰克尔式共轭条件的第二类混合方程的比萨泽-萨马尔斯基式非局部边界问题

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600626

B. I. Islomov, A. A. Abdullayev

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引用次数: 0

摘要

摘要研究对象是具有非局部条件的第二类椭圆-双曲型方程的边界值问题的可解性。边界值问题的特征被任意分为两部分，其中一部分给出了 Bitsadze-Samarsky 条件。第二部分不受边界条件的限制，缺失的比萨泽-萨马尔斯基条件由退化区间上的类似弗兰克尔条件代替。利用极值原理方法证明了问题解的唯一性。利用奇异积分方程理论和维纳-霍普夫方程证明了问题解的存在性。因此，提出并证明了所提问题的可解性定理。

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Bitsadze–Samarsky Type Nonlocal Boundary Value Problem for a Second Kind Mixed Equation with a Conjugation Condition of the Frankl Type

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.

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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.