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In this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study a mathematical model which describes the quasistatic frictional contact between aviscoplastic body and a foundation. The contact is modeled with normal compliance, unilateral constraint, friction, damage andmemory term, which also includes foundation memory property. We present the classical formulation of the problem and derivevariational-hemivariational formulation. Finally we provide a unique weak solution of the problem. [ABSTRACT FROM AUTHOR]

The goal of this paper is to deal with approximate controllability of control systems described by non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions in Hilbert spaces. First we define the concept of mild solution relying on the existence of an evolution operator for the corresponding linear equation and the property of Clarke subdifferential. Next, the solvability and approximate controllability are considered by means of a fixed-point strategy. Finally, two examples are provided to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper studies a system of two hemivariational inequalities modeling a dynamic thermoviscoelastic contact problem with general nonmonotone and multivalued subdifferential boundary conditions. Thermal effects are included in the Kelvin-Voigt thermoviscoelastic constitutive law and in the boundary conditions, and so in frictional heat generation, which takes place on the boundary and enters the condition for the temperature. The existence of a weak solution to the problem is established using a recent surjectivity result for differential inclusions associated with pseudomonotone operators. [ABSTRACT FROM AUTHOR]

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of thep-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique. [ABSTRACT FROM PUBLISHER]

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be dynamic and the material behavior is described by a elastic–viscoplastic constitutive law with damage. The frictional contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the displacement and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of hyperbolic hemivariational inequality, a classical existence, and uniqueness result on parabolic inequalities and a fixed point argument. [ABSTRACT FROM AUTHOR]

We consider a class of identification problems for a non-linear parabolic boundary hemivariational inequality. Using the least square cost functionals, the problem is to identify an unknown coefficient which depends on the gradient of the solution. It is shown that the hemivariational inequality admits a unique weak solution, which depends continuously on the coefficient. The boundary condition is of a subdifferential type with non-convex and non-smooth potential. Existence of solutions to the inverse problems is established by using the direct method. [ABSTRACT FROM AUTHOR]

We are concerned with two classes of non-standard hemivariational inequalities. In the first case we establish a Hartman-Stampacchia type existence result in the framework of stably pseudomonotone operators. Next, we prove an existence result for a class of non-linear perturbations of canonical hemivariational inequalities. Our analysis includes both the cases of compact sets and of closed convex sets in Banach spaces. Applications to non-coercive hemivariational and variational-hemivariational inequalities illustrate the abstract results of this article. [ABSTRACT FROM AUTHOR]

We prove existence results for multivalued quasilinear elliptic problems of hemivariational inequality type with measure data right-hand sides. In case of L1-data, we study existence and enclosure behaviors of solutions by an appropriate sub-supersolution approach. The proofs of our results are based on general existence theory for multivalued pseudomonotone operators, and approximation-, truncation-, and special test function techniques. [ABSTRACT FROM AUTHOR]

In this article we examine an evolution problem, which describes the dynamic contact of a viscoelastic body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. First we derive a formulation of the model in the form of a multidimensional hemivariational inequality. Then we establish a priori estimates and we prove the existence of weak solutions by using a surjectivity result for pseudomonotone operators. Finally, we deliver conditions under which the solution of the hemivariational inequality is unique. [ABSTRACT FROM AUTHOR]

We give an existence result for a double eigenvalue problem in Hemivariational Inequalities whose energetic functional is not locally Lipschitz. It is used a finite dimensional approach based on Kakutani's fixed point theorem. [ABSTRACT FROM AUTHOR]