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Control in obstacle pseudoplate problem
Author(s) -
Lovíšek J.
Publication year - 2006
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.200310273
Subject(s) - variational inequality , mathematics , obstacle problem , subsequence , sequence (biology) , rigidity (electromagnetism) , optimal control , zero (linguistics) , obstacle , state (computer science) , boundary (topology) , limit of a sequence , basis (linear algebra) , mathematical optimization , existence theorem , mathematical analysis , limit (mathematics) , geometry , algorithm , structural engineering , linguistics , philosophy , biology , political science , law , engineering , bounded function , genetics
The paper is concerned with the study of an optimal control problem for elastic plate with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is governed by a semi‐coercive variational inequality. As unique solvability of the state problem is guaranteed, the existence of an optimal control can be proven on abstract level. The approximate optimization problems are introduced, making use of finite element method. The solvability of the approximate problems is proved on the basis of the general theorem. When the mesh‐size tends to zero, then a subsequence of any sequence of approximate solutions converges to a solution of the continuous problem.