报告题目：History-dependent  Variational-hemivariational  Inequalities  in Contact Mechanics

报告时间：2018年10月25日，星期四，上午10:10-12:00

报告地点：数学楼112

报告人：Mircea Sofonea，University of Perpignan Via Domitia, France

报告摘要：

We present recent results in the study of variational-hemivariational inequalities with applications to Contact Mechanics. We start by introducing the concept of history-dependent operator together with relevant examples in analysis, ordinary differential equations and mechanics. Then, we state and prove an existence and uniqueness result for a class of variational-hemivariational inequalities with history-dependent operators, the so-called history-dependent inequalities. The proof is based on arguments of pseudomonotonicity and fixed point. Under additional assumptions, we proceed with the study of the behavior of the solution with respect to the set of constraints and prove a continuous dependence result. To this end we use various estimates, monotonicity arguments and the properties of the Clarke subdifferential.

Next, we consider a mathematical model which describes the equilibrium of a locking material with memory, in contact with an obstacle. We comment the model and state its weak formulation, which is in a form of a history-dependent variational hemivariational inequality for the displacement field. We use our abstract results to prove the unique weak solvability of the model and the continuous dependence of the solution with respect to the set of constraints. We apply this convergence result in the study of an optimization problem associated to the contact model. Finally, we list additional results concerning the numerical analysis of history-dependent variational-hemivariational inequalities and provide numerical simulations in the study of a second mathematical model which describes the contact between an elastic body with  a rigid-deformable foundation.

报告人简介：

Mircea Sofonea，于1988在罗马尼亚布加勒斯特大学获得数学博士学位，现任法国佩皮尼昂大学正教授，物理和数学实验室主任。Sofonea教授是非线性分析、偏微分方程理论及其应用领域的国际著名专家，已在国际学术期刊发表论文200多篇，撰写学术专著8本。