Related papers: Optimal control of differential quasivariational i…

The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…

We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…

This paper is devoted to a study of time-dependent hemivariational inequality. We prove existence and uniqueness of its solution, provide fully discrete scheme and reformulate this scheme as a series of nonsmooth optimization problems. This…

We consider a mathematical model which describes the quasistatic frictionless contact of a viscoelastic body with a rigid-plastic foundation. We describe the mechanical assumptions, list the hypotheses on the data and provide three…

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic…

This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…

In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator,…

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact…

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational…

In this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation. We employ the nonlinear constitutive viscoelastic law with…

The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…

This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact…

A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

The purpose of this paper is three-fold. Firstly we attack a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions. The investigated problem involves a nonlinear monotone partial differential…

In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases.…

The overarching goal of this paper is to introduce and investigate a new nonlinear system driven by a nonlinear differential equation, a history-dependent quasivariational inequality, and a parabolic variational inequality in Banach spaces.…

We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…

Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…