首页|Optimal control of differential quasivariational-hemivariational inequalities with applications
Optimal control of differential quasivariational-hemivariational inequalities with applications
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In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.
differential variational-hemivariational inequalityunilateral constrainthistory-dependent opera-toroptimal controltime-optimal controlmaximum stay problem
Dong-ling Cai、Stanisław Migórski、Yi-bin Xiao
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School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China
College of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,China
Chair of Optimization and Control,Jagiellonian University in Krakow,Krakow 30348,Poland
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