Optimal Control of History-Dependent Evolution Inclusions with Applications to Frictional Contact

Stanisław Migórski ()
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Stanisław Migórski: Chengdu University of Information Technology

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 14, 574-596

Abstract: Abstract In this paper, we study a class of subdifferential evolution inclusions involving history-dependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example of an optimal control of a dynamic frictional contact problem in mechanics, whose weak formulation is the evolution variational inequality.

Keywords: Optimal control; Evolution inclusion; Variational inequality; History-dependent operator; Frictional contact; 49A22; 49J24; 49J27; 35K86; 35L86; 73T05; 74M10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01659-0

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