Turkish Journal of Mathematics
Author ORCID Identifier
MANAL ALOTAIBI: 0000-0003-4360-4448
NASSER-EDDINE TATAR: 0000-0003-3467-230X
WALED AL-KHULAIF: 0000-0003-0746-4265
Abstract
This paper investigates the exponential stability of a strongly damped wave equation subject to an internal distributed time delay. Two distinct analytical frameworks are developed: the first employs a modified energy method based on auxiliary functionals, while the second introduces a transformation that rewrites the delay term as the derivative of a convolution integral. Both approaches yield explicit decay conditions and establish exponential convergence of the energy under weaker assumptions on the damping coefficient and the delay kernel. Notably, the transformation method allows for a wider class of admissible delay weights than those permitted by classical techniques. Numerical simulations based on a finite difference scheme are presented to validate the theoretical results and to compare the performance of the two methods. These findings contribute to the qualitative theory of delayed hyperbolic systems and the stabilization of wave equations with memory effects.
DOI
10.55730/1300-0098.3779
Keywords
Strongly damped wave equation, distributed delay, exponential stability, Lyapunov functional, energy method
First Page
1008
Last Page
1030
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
ALOTAIBI, M, TATAR, N, & AL-KHULAIF, W (2026). Exponential stability for a strongly damped wave equation with distributed internal delay. Turkish Journal of Mathematics 50 (5): 1008-1030. https://doi.org/10.55730/1300-0098.3779
