Neumann problem for the Lavrent’ev–Bitsadze equation with two type-change lines in a rectangular domain
- Authors: Gimaltdinova A.A.1,2
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Affiliations:
- Sterlitamak Branch
- Institute of Applied Studies
- Issue: Vol 93, No 1 (2016)
- Pages: 1-5
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223341
- DOI: https://doi.org/10.1134/S1064562416010038
- ID: 223341
Cite item
Abstract
The Neumann problem for an equation with two perpendicular internal type-change lines in a rectangular domain is investigated. Uniqueness and existence theorems are proved by applying the spectral method. The separation of variables yields an eigenvalue problem for an ordinary differential equation. This problem is not self-adjoint, and the system of its eigenfunctions is not orthogonal. A corresponding biorthogonal system of functions is constructed and proved to be complete. The completeness result is used to prove a necessary and sufficient uniqueness condition for the problem under study. Its solution is constructed in the form of the sum of a biorthogonal series.
About the authors
A. A. Gimaltdinova
Sterlitamak Branch; Institute of Applied Studies
Author for correspondence.
Email: alfiragimaltdinova@mail.ru
Russian Federation, pr. Lenina 49, Sterlitamak, 453103; Odesskaya ul. 68, Sterlitamak, 453103