On a dynamic frictional contact problem with normal damped response and long-term memory

Abstract

A dynamic frictional contact problem between a viscoelastic body and a foundation is studied. The contact is modeled with normal damped response and a friction law. The constitutive law with long memory is assumed to be nonlinear. The existence result is proved using nonlinear monotone operators, fixed point argument, and extension procedure. Moreover, the exponential stability of the energy solution is established using the multiplier method.

Exponential stabilization of a dynamic frictional contact problem for viscoelastic materials with normal damped response and infinite memory

“…Matei and Ciurcea [27] proved the weak solvability of a contact problem with memory where the elastic operator can be nonlinear. Recently, Ouakil et al [35] studied the stability of a dynamic frictional contact problem between a viscoelastic body and a foundation, and the contact is modeled with normal damped response and a friction law. Note that the long-memory considered in [41,27,35] is finite.…”

“…Recently, Ouakil et al [35] studied the stability of a dynamic frictional contact problem between a viscoelastic body and a foundation, and the contact is modeled with normal damped response and a friction law. Note that the long-memory considered in [41,27,35] is finite. When limited to the finite memory setting, the system does not generate a semigroup.…”

“…Whereas the infinite delay model can be represented as a semigroup evolution with the help of appropriately defined historical variables. In this paper, we consider a dynamic frictional contact problem with a normal damped response and infinite memory, which leads to a new mathematical model, different to the one presented in [41,27,35]. To the best knowledge of the authors, it has not been considered.…”