On the Decay and Global Existence of Solutions to a Nonlinearly Damped Wave Equation with Variable Exponents and Delay - Kafini, Mohammad; Al-Mahdi, Adel M.; Al-Gharabli, Mohammad M. (Journal of Applied Nonlinear Dynamics, 2026)
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.