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Recovery of unknown coefficients in a two-dimensional hyperbolic equation with additional conditions
  • Elvin Azizbayov,
  • He Yang,
  • Yashar Mehraliyev
Elvin Azizbayov
Academy of Public Administration under the President of the Republic of Azerbaijan

Corresponding Author:[email protected]

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He Yang
Augusta University
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Yashar Mehraliyev
Baku State University
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In this paper, a nonlocal inverse boundary value problem for a two-dimensional hyperbolic equation with overdetermination conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method, solving an equivalent problem is reduced to solving a system of integral equations and by the contraction mappings principle the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the uniquely existence theorem for the classical solution of the considered inverse problem is proved and some considerations on the numerical solution for this inverse problem are presented with the examples.
20 Jul 2021Submitted to Mathematical Methods in the Applied Sciences
21 Jul 2021Submission Checks Completed
21 Jul 2021Assigned to Editor
07 Aug 2021Reviewer(s) Assigned
06 Mar 2022Editorial Decision: Revise Minor
19 Mar 20221st Revision Received
21 Mar 2022Submission Checks Completed
21 Mar 2022Assigned to Editor
23 Mar 2022Reviewer(s) Assigned
29 Jun 2022Review(s) Completed, Editorial Evaluation Pending
21 Jul 2022Editorial Decision: Accept