Email this article On a discrete boundary value problem in a quarter-plane
- Authors: Vasilyev V.B.1, Mashinets A.A.2
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Affiliations:
- 308015, Российская Федерация, г. Белгород, ул. Победы, 85
- Belgorod National Research University
- Issue: Vol 28, No 142 (2023)
- Pages: 169-181
- Section: Original articles
- URL: https://ogarev-online.ru/2686-9667/article/view/296354
- ID: 296354
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Abstract
We study the solvability of a discrete analogue of a model pseudo-differential equation in a quarter-plane in discrete Sobolev–Slobodetskii spaces. Using a concept of periodic wave factorization for elliptic periodic symbol, we describe solvability conditions for the equation and for a certain boundary value problem related to this equation. In particular, for certain values of the index of periodic wave factorization, a formula for a general solution of the model discrete pseudo-differential equation is obtained, there are some arbitrary functions in the formula. For their unique determination, we introduce certain additional conditions such as a discrete analogues of integral conditions on angle sides. The existence and uniqueness theorem for the stated boundary value problem is proved and a priori estimates for the solution are obtained. A comparison between discrete and continuous solutions for a special choice of discrete objects is also given.
About the authors
Vladimir B. Vasilyev
308015, Российская Федерация, г. Белгород, ул. Победы, 85
Author for correspondence.
Email: vbv57@inbox.ru
ORCID iD: 0000-0001-9351-8084
Doctor of Physics and Mathematics, Head of Applied Mathematics And Computer Modeling Department
Russian Federation, 85 Pobedy St., Belgorod 308015, Russian FederationAnastasia A. Mashinets
Belgorod National Research University
Email: anastasia.kho@yandex.ru
ORCID iD: 0000-0003-2440-8556
Post-Graduate Student, Applied Mathematics and Computer Modeling Department
Russian Federation, 85 Pobedy St., Belgorod 308015, Russian FederationReferences
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