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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On the Decay and Global Existence of Solutions to a Nonlinearly Damped Wave Equation with Variable Exponents and Delay

Journal of Applied Nonlinear Dynamics 14(4) (2025) 899--911 | DOI:10.5890/JAND.2025.12.015

Mohammad Kafini, Adel M. Al-Mahdi, Mohammad M. Al-Gharabli

Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

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Abstract

In this paper, we consider a nonlinear wave equation with variable exponents and time-varying delay. We prove a global existence result using the well depth method and by a lemma by Komornik, we establish the decay estimates for the solution under suitable assumptions on the variable exponents $m,p$ and the initial data. This work generalizes and extends several works in the literature.

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