On the stability of Bresse system with one discontinuous local internal Kelvin–Voigt damping on the axial force

In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping Kelvin-Voigt type acting on axial force, under fully Dirichlet boundary conditions. First, using general criteria Arendt-Batty, prove strong stability our system. Finally, frequency domain approach combined multiplier method, that energy decays polynomially different rates.