Abstract
In this paper, an abstract evolutionary hemivariational inequality with a history-dependent operator is studied. First, a result on its unique solvability and solution regularity is proved by applying the Rothe method. Next, we introduce a numerical scheme to solve the inequality and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modeled with a viscoelastic constitutive law, the contact is given in the form of multivalued normal compliance, and friction is described with a subgradient of a locally Lipschitz potential. Finally, for the contact problem, we provide the optimal error estimate.
Highlights
In this paper, we are concerned with the existence and uniqueness of a solution to an abstract evolutionary hemivariational inequality which involves a history-dependent operator of the formAu (t) + Bu(t) + (Ru)(t) − f (t), v + J 0(Mu(t); Mv) ≥ 0 (1)for all v ∈ V, a.e. t ∈ (0, T ) with u(0) = u0
We apply the results to a quasistatic frictional contact problem in which the material is modeled with a viscoelastic constitutive law, the contact is given in the form of multivalued normal compliance, and friction is described with a subgradient of a locally Lipschitz potential
We are concerned with the existence and uniqueness of a solution to an abstract evolutionary hemivariational inequality which involves a history-dependent operator of the form
Summary
We are concerned with the existence and uniqueness of a solution to an abstract evolutionary hemivariational inequality which involves a history-dependent operator of the form. The hemivariational inequality (1) without a history-dependent operator has been recently investigated in [24] by using the vanishing acceleration method, where a local existence result was proved. We provide the variational formulation of the contact problem for which we deliver a result on its unique weak global solvability. In this way, we improve the local existence result of [24, Theorem 17].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
