Recovery of the unknown coefficients in a two-dimensional hyperbolic equation

Yashar T. Mehraliyev, He Yang, Elvin I. Azizbayov

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, an 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 to the original problem in a certain sense. We then use the Fourier method to reduce such an equivalent problem to a system of integral equations. Furthermore, we prove the existence and uniqueness theorem for the auxiliary problem by the contraction mappings principle. Based on the equivalency of these problems, the existence and uniqueness theorem for the classical solution of the original inverse problem is proved. Some discussions on the numerical solutions for this inverse problem are presented including some numerical examples.

Original languageEnglish (US)
JournalMathematical Methods in the Applied Sciences
DOIs
StateAccepted/In press - 2022

Keywords

  • Fourier method
  • classical solution
  • inverse coefficient problem
  • overdetermination condition
  • two-dimensional hyperbolic equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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