EXISTENCE, UNIQUENESS, AND CONTINUOUS DEPENDENCE OF THE SOLUTION TO A HYPERBOLIC EQUATION WITH AN UNKNOWN COEFFICIENT

Meriem Saker; Iqbal M. Batiha; Areen Al-Khateeb; Taki Eddine Oussaeif; Nidal Anakira

doi:10.56947/gjom.v22i2.4102

EXISTENCE, UNIQUENESS, AND CONTINUOUS DEPENDENCE OF THE SOLUTION TO A HYPERBOLIC EQUATION WITH AN UNKNOWN COEFFICIENT

Meriem Saker
, Iqbal M. Batiha
, Areen Al-Khateeb
, Taki Eddine Oussaeif
, Nidal Anakira

Nonlinear Dynamic Research Centre (NDRC)

Abbès Laghrour University of Khenchala
Al-Zaytoonah University of Jordan
Jadara University
University of L’aarbi Ben M’Hidi
Sohar University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the existence, uniqueness, and continuous dependence of the solution for a hyperbolic equation arising in the framework of inverse problems. To achieve this, we first prove the existence and uniqueness of the solution to the associated direct problem using the energy inequality method. Then, by means of fixed point theory, we establish the existence and uniqueness of the solution to the inverse problem.

Original language	English
Journal	Gulf Journal of Mathematics
Volume	22
Issue number	2
DOIs	https://doi.org/10.56947/gjom.v22i2.4102
State	Published - 30 Mar 2026

Keywords

Fixed point theorem
Inverse nonlinear problem
Nonlinear hyperbolic equation
nonlocal integral condition

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10.56947/gjom.v22i2.4102

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title = "EXISTENCE, UNIQUENESS, AND CONTINUOUS DEPENDENCE OF THE SOLUTION TO A HYPERBOLIC EQUATION WITH AN UNKNOWN COEFFICIENT",

abstract = "In this paper, we study the existence, uniqueness, and continuous dependence of the solution for a hyperbolic equation arising in the framework of inverse problems. To achieve this, we first prove the existence and uniqueness of the solution to the associated direct problem using the energy inequality method. Then, by means of fixed point theory, we establish the existence and uniqueness of the solution to the inverse problem.",

keywords = "Fixed point theorem, Inverse nonlinear problem, Nonlinear hyperbolic equation, nonlocal integral condition",

author = "Meriem Saker and Batiha, \{Iqbal M.\} and Areen Al-Khateeb and Oussaeif, \{Taki Eddine\} and Nidal Anakira",

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AU - Saker, Meriem

AU - Batiha, Iqbal M.

AU - Al-Khateeb, Areen

AU - Oussaeif, Taki Eddine

AU - Anakira, Nidal

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2026/3/30

Y1 - 2026/3/30

N2 - In this paper, we study the existence, uniqueness, and continuous dependence of the solution for a hyperbolic equation arising in the framework of inverse problems. To achieve this, we first prove the existence and uniqueness of the solution to the associated direct problem using the energy inequality method. Then, by means of fixed point theory, we establish the existence and uniqueness of the solution to the inverse problem.

AB - In this paper, we study the existence, uniqueness, and continuous dependence of the solution for a hyperbolic equation arising in the framework of inverse problems. To achieve this, we first prove the existence and uniqueness of the solution to the associated direct problem using the energy inequality method. Then, by means of fixed point theory, we establish the existence and uniqueness of the solution to the inverse problem.

KW - Fixed point theorem

KW - Inverse nonlinear problem

KW - Nonlinear hyperbolic equation

KW - nonlocal integral condition

UR - https://www.scopus.com/pages/publications/105034656184

U2 - 10.56947/gjom.v22i2.4102

DO - 10.56947/gjom.v22i2.4102

M3 - Article

AN - SCOPUS:105034656184

SN - 2309-4966

VL - 22

JO - Gulf Journal of Mathematics

JF - Gulf Journal of Mathematics

IS - 2

ER -

EXISTENCE, UNIQUENESS, AND CONTINUOUS DEPENDENCE OF THE SOLUTION TO A HYPERBOLIC EQUATION WITH AN UNKNOWN COEFFICIENT

Abstract

Keywords

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