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Boundary optimal control of a dynamic frictional contact problem
Author(s) -
Peng Zijia,
Gamorski Piotr,
Migórski Stanisław
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900144
Subject(s) - variational inequality , viscoelasticity , boundary (topology) , coulomb friction , optimal control , mathematics , dry friction , coulomb , boundary value problem , coulomb's law , control (management) , mathematical analysis , control theory (sociology) , classical mechanics , mathematical optimization , physics , nonlinear system , computer science , materials science , quantum mechanics , artificial intelligence , composite material , thermodynamics , electron
In this paper we study boundary optimal control of an evolutionary system governed by a history‐dependent variational‐hemivariational inequality. The inequality is a weak formulation of a dynamic frictional contact problem for a viscoelastic body with a multivalued normal damped response condition and a simplified version of the Coulomb law of dry friction. A continuous dependence result for the solution map is proved and the existence of optimal solutions to the control problem is established.