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Penalty and regularization method for variational‐hemivariational inequalities with application to frictional contact
Author(s) -
Migórski Stanisław,
Zeng Shengda
Publication year - 2018
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.201700348
Subject(s) - uniqueness , differentiable function , mathematics , regularization (linguistics) , variational inequality , constraint (computer aided design) , convergence (economics) , coulomb friction , coulomb , coulomb's law , inequality , mathematical analysis , nonlinear system , computer science , physics , geometry , quantum mechanics , artificial intelligence , economics , economic growth , electron
In this paper, we provide results on existence, uniqueness and convergence for a class of variational‐hemivariational inequalities of elliptic type involving a constraint set and a nondifferentiable potential. We introduce a penalized and regularized problem without constraints and with G a ̂ teaux differentiable potential. We prove that the solution to the original problem can be approached, as a parameter converges, by the solution of the approximated problem. An application to frictional contact problem with the Signorini contact condition and a static version of the Coulomb friction law illustrates the results.