Well-posedness and exponential stability for abstract evolution equations with delay in the nonlinear source: frictional and viscoelastic cases

In this paper, we establish the well-posedness and exponential stability of a class of semilinear neutral abstract evolution equations with constant time delay. Two damping mechanisms are considered: frictional damping of the form $CC^*u_t$ and viscoelastic damping with memory. Under suitable assump