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On the solvability of dynamic elastic‐visco‐plastic contact problems
Author(s) -
Jarušek J.,
Sofonea M.
Publication year - 2008
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.200710360
Subject(s) - mathematics , monotone polygon , compact space , a priori and a posteriori , variational inequality , regularization (linguistics) , weak formulation , nonlinear system , mathematical analysis , limit point , constraint (computer aided design) , obstacle , boundary value problem , computer science , geometry , physics , philosophy , epistemology , quantum mechanics , artificial intelligence , political science , law
We consider two dynamic contact problems between an elastic‐visco‐plastic body and an obstacle, the so‐called foundation. The contact is frictionless and it is modelled with normal compliance of such a type that the penetration is not restricted in the first problem, but is restricted with unilateral constraint, in the second one. We derive a variational formulation of the first problem and then prove its unique weak solvability, by using arguments on nonlinear evolution equations with monotone operators and fixed point. Then, we derive a variational formulation of the second problem and prove its weak solvability. To this end we consider a sequence of regularized problems which have a unique solution, derive a priori estimates and use compactness properties to obtain a solution to the original model, by passing to the limit as the regularization parameter converges to zero.