Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term - Kechiche, Dounya; Khemmoudj, Ammar; Medjden, Mohammed (Mathematical methods in the applied sciences, 2024)
In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function b(x)≥0$$ b(x)\ge 0 $$ with dynamic Wentzell boundary conditions and delay term. By using frequency domain approach method, we show that under a suitable assumption between the internal damping function c$$ c $$ and the boundary delay feedback, considering some geometrical assumptions on the boundary of Ω$$ Ω $$, supposing that the relaxation function h$$ h $$ decay exponentially to zero, that the energies of the problem decay exponentially to zero.