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A shape-topological control of variational inequalities. (English) Zbl 1463.35062

Summary: 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.

MSC:

35B25 Singular perturbations in context of PDEs
49J40 Variational inequalities
49Q10 Optimization of shapes other than minimal surfaces
74G70 Stress concentrations, singularities in solid mechanics
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