On Solvability of An Inverse Boundary Value Problem For The Elliptic Equation Of Second Order With Periodic And Integral Condition
Abstract
An inverse boundary value problem for a
second-order elliptic equation with periodic and integral condition is
investigated. The definition of a classical solution of the problem is
introduced. The goal of this paper is to determine the unknown coefficient and
to solve the problem of interest. The problem is considered in a rectangular
domain. To investigate the solvability of the inverse problem, we perform a
conversion from the original problem to some auxiliary inverse problem with
trivial boundary conditions. By the contraction mapping principle we prove the
existence and uniqueness of solutions of the auxiliary problem. Then we make a
conversion to the stated problem again and, as a result, we obtain the
solvability of the inverse problem.
Keywords
References
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- [4] Ivanov V.K., Vasin V.V., Tanana V.P., Theory of linear ill-posed problems and its applications, M., Nauka, 1978 (in Russian).
- [5] Denisov A.M., Introduction to theory of inverse problems, M., MGU, 1994 (in Russian).
- [6] Mehraliyev Ya.T., On solvability of an inverse boundary value problem for a second order elliptic equation, Vest. Tverskogo Gos. Univ., Ser. prikladnaya matematika, (2011), no. 23, 25–38 (in Russian).
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Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Rauf Amırov
*
0000-0001-6754-2283
Türkiye
Y.t. Mehralıyev
0000-0002-2054-3219
N.a. Heydarzade
Publication Date
June 30, 2019
Submission Date
November 29, 2018
Acceptance Date
March 19, 2019
Published in Issue
Year 2019 Volume: 40 Number: 2
Cited By
On the Solvability of an Inverse Boundary Value Problem for a Second‐Order Hyperbolic Equation With a Memory Term
Mathematical Methods in the Applied Sciences
https://doi.org/10.1002/mma.70418