Uniform Decay for the Viscoelastic Kirchhoff-Type Equations with Memory and Delay Terms

In this paper, we investigate the initial boundary value problem of the viscoelastic Kirchhoff-type equations with memory and delay terms. We investigate the initial boundary value problem of viscoelastic Kirchhoff-type equations with memory and delay terms. The analysis assumes relatively weak conditions for the relaxation function g. This paper introduces a new framework for analyzing decay properties under weaker conditions, improving upon previous results in the literature. Finally, we prove that the system energy exhibits exponential and polynomial decay rates, which depend on the behavior of the relaxation function ɡ. This provides new insights into the energy decay properties of Kirchhoff-type viscoelastic wave equations under weaker conditions on the relaxation function, and provides a valuable technical framework for exploring the decay properties of more complex partial differential equations.