A fully dynamic frictional contact problem for viscoelastic materials with long-term memory and simplified Coulomb’s friction law

We study a mathematical model describing the dynamic behavior of a viscoelastic body in frictional contact with a rigid foundation. The contact is governed by simplified Coulomb’s friction law, and the material exhibits a nonlinear constitutive law incorporating long-term memory effects. We present the model, specify the assumptions on the data, and derive a variational formulation in terms of the displacement field. We first establish a local existence and uniqueness result, then the global existence result is proved via energy methods. Finally, we prove the exponential stability of energy solutions using the multiplier technique.