New stability result of a partially dissipative viscoelastic Timoshenko system with a wide class of relaxation function

This paper is concerned with the following partially dissipative viscoelastic Timoshenko system {rho(1)phi(tt) = kappa(phi(x) + psi)(x) +kappa(t)(integral 0)g(t-s)(phi(x)+psi)(x) ds = 0 in (0, L) x R+, rho(2)psi(tt) - b psi(xx) + kappa(phi x+psi) - kappa integral(t)(0) g(t-s)(phi(x)+psi) ds =0 in (0, L) x R+, with damping mechanism acting only on the shear force, and with Dirichlet boundary conditions. We consider a very general relaxation function g'(t) <= -xi(t)H(g(t)), for all >= 0. Under appropriate conditions on. and H, we establish a general stability result. The result is obtained under the assumption of equal speed of wave propagation. This work extends and generalizes many results in literature such as Alves et al. [On modeling and uniform stability of a partially dissipative viscoelastic Timoshenko system. SIAM J Math Anal. 2019;51(6):4520-4543].