This article is cited in 3 papers

A shape-topological control of variational inequalities

V. A. Kovtunenko^ab, G. Leugering<sup>c

a</sup> Lavrent'ev Institute of Hydrodynamics, 630090 Novosibirsk, Russia
^b Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria
^c Applied Mathematics 2, Friedrich-Alexander University of Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany

Abstract: A shape-topological control of singularly perturbed variational inequalities is considered in the abstract framework for state-constrained optimization problems. Aiming at asymptotic analysis, singular perturbation theory is applied to the geometry-dependent objective function and results in a shape-topological derivative. This concept is illustrated analytically in a one-dimensional example problem which is controlled by an inhomogeneity posed in a domain with moving boundary.

Keywords and phrases: shape-topological control, state-constrained optimization, variational inequality, singular perturbation, inhomogeneity, shape-topological derivative.

MSC: 35B25, 49J40, 49Q10, 74G70

Received: 14.03.2016

Language: English

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