Minimax Theory and its Applications 09 (2024), No. 2, 253--270
Copyright Heldermann Verlag 2024
Analysis and Control of a General Elliptic Quasivariational-Hemivariational Inequality
Weimin Han
Department of Mathematics, University of Iowa, Iowa City, U.S.A.
weimin-han@uiowa.edu
Mircea Sofonea
Laboratory of Mathematics and Physics, University of Perpignan, Perpignan, France
sofonea@univ-perp.fr
We consider a general elliptic quasivariational-hemivariational inequality in real Hilbert spaces for which we provide a solution existence and uniqueness result, a convergent iterative procedure, and a Lipschitz continuous dependence result that we use in order to deduce the existence of a solution to an associated optimal control problem. As an example for applications of the abstract results, we consider a new model of static contact problem which describes the equilibrium of an elastic body with a reactive foundation. The weak formulation of the model is a quasivariational-hemivariational inequality for the displacement field. We present theoretical results on the analysis and control of the contact problem.
Keywords: Quasivariational-hemivariational inequality, existence, uniqueness, optimal control, locking material, frictional contact problem, unilateral constraint, weak solution.
MSC: 35J87, 47J20, 49J21, 74M10, 74M15.
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