Stabilization of a coupled wave equation with one localized nonregular fractional Kelvin–Voigt damping with nonsmooth coefficients

Abstract

In this paper, we study the stabilization of a coupled wave system formed by one localized nonregular fractional viscoelastic damping of Kelvin–Voigt type and localized nonsmooth coefficients. Our main aim is to prove that the ‐semigroup associated with this model is strong stability and decays polynomially at a rate of . By introducing a new system to deal with fractional Kelvin–Voigt damping, we obtain a new equivalent augmented system, so as to show the well‐posedness of the system based on Lumer–Phillips theorem. We achieve the strong stability for the ‐semigroup associated with this new model by using a general criteria of Arendt–Batty and then turn out a polynomial energy decay rate of order with the help of a frequency domain approach.