A new class of fractional impulsive differential hemivariational inequalities with an application

Hemivariational Inequalities on Graphs

In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke's subdifferential. First of all, we state and prove some results on the subdifferentiability of nonconvex functionals defined on graphs. Thereafter, an elliptic hemivariational inequality on locally finite graphs is considered and the existence and uniqueness of its weak solutions are proved by means of the well-known surjectivity result for pseudomonotone mappings. In the end of this pa…

Calmness of the solution mapping of Navier-Stokes problems modeled by hemivariational inequalities

The main purpose of this paper is to find conditions for Holder calmness of the solution mapping, viewed as a function of the boundary data, of a hemivariational inequality governed by the Navier-Stokes operator. To this end, a more abstract model is studied first: a class of parametric equilibrium problems defined by trifunctions. The presence of trifunctions allows the extension of the monotonicity notions and of the duality principle in the theory of equilibrium problems.

一类分数阶半变分不等式的存在性与近似能控性

Existence And Approximate Controllability for a class of Fractional Order Hemivariational Inequalities

针对 Hilbert 空间中非线性半变分不等式驱动的分数阶微分控制问题，利用非光滑分析和不动点方法证明温和解存在，并基于线性系统近似能控建立充分条件。

Distributed optimal control problems for a class of elliptic hemivariational inequalities with a parameter and its asymptotic behavior

In this paper, we study optimal control problems on the internal energy for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction problem with non-monotone multivalued subdifferential boundary condition on a portion of the boundary of the domain described by the Clarke generalized gradient of a locally Lipschitz function. We prove an existence result for the optimal controls and we show an asymptotic result for the optimal controls and the system states, when the parameter, like a heat t…

On optimal control in a nonlinear interface problem described by hemivariational inequalities

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 equation in the interior domain and the Laplacian in the exterior domain. Such a scalar interface problem models nonmonotone frictional contact of elastic infinite media. The variational formulation of the interface problem leads to a hemivariational inequality (HVI), which however lives on the unbounded domain, and thus cannot analyzed in a reflexive Banac…

基于相场方法的结构半变分不等式接触问题形状设计

Shape design with phase field methods for structural hemivariational inequalities in contact problems

本文提出基于相场方法的结构半变分不等式接触问题形状设计与拓扑优化新方法，通过非凸半变分不等式模型和正则化技术实现摩擦接触问题的高效优化。