An Inverse Problem for a Parabolic Equation with Nonlocal Boundary Conditions and Two-point Overdetermination

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6796

Keywords:

Inverse problem, Parabolic equation, Nonlocal conditions, Classical solution, Existence, Uniqueness

Abstract

This paper is devoted to the study of an inverse boundary value problem for a parabolic equation with nonlocal boundary conditions and two-point overdetermination. To analyze the solvability of the problem, we first consider the associated auxiliary inverse boundary value problem. Applying the Fourier method, the solution of the equivalent problem is reduced to a system of integral equations, and the existence and uniqueness of the solution to the auxiliary problem is proved using the contraction mapping principle in an appropriate functional space. Further, using the equivalence, the existence and uniqueness theorem for the classical solution of the original problem is proved.

Author Biographies

  • Elvin Ibrahim Azizbayov, The Academy of Public Administration under the President of the Republic of Azerbaijan

    Elvin I. Azizbayov - Doctor of Sciences on Mathematics, Professor, Head of the Department of Intelligent Systems Management, The Academy of Public Administration under the President of the Republic of Azerbaijan, 74 Lermontov street, Baku, AZ1001, Azerbaijan; e-mail: [email protected] ; https://orcid.org/0000-0002-1164-953X.

  • Aynur Safarova, Institute of Mathematics and Mechanics

    Senior researcher, Department of Functional Analysis, Institute of Mathematics and Mechanics, Baku, Azerbaijan

Downloads

Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Differential Equations

License

Copyright (c) 2025 Elvin Ibrahim Azizbayov, Aynur Safarova

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

An Inverse Problem for a Parabolic Equation with Nonlocal Boundary Conditions and Two-point Overdetermination. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6796. https://doi.org/10.29020/nybg.ejpam.v18i4.6796