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Existence and relaxation results for nonlinear second order evolution inclusions

100%
Migórski S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
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tom 15
|
nr 2
129-148
EN
In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.
2
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Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

100%
Migórski S.
Open Mathematics
|
2012
|
tom 10
|
nr 6
1953-1968
EN
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.
3
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Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities

51%
Denkowski Z., Migórski S.
Control and Cybernetics
|
2004
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tom 33
|
nr 2
211-236
4
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Optimal control for a class of mechanical thermoviscoelastic frictional contact problems

45%
Denkowski Z., Migórski S., Ochal A.
Control and Cybernetics
|
2007
|
tom 36
|
nr 3
611-632
5
Content available remote

A hybrid algorithm for solving inverse problems in elasticity

39%
Barabasz B., Gajda-Zagórska E., Migórski S., Paszyński M., Schaefer R., Smołka M.
International Journal of Applied Mathematics and Computer Science
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2014
|
tom 24
|
nr 4
865-886
EN
The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.
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