A Shape-Topological Control of Variational Inequalities - Kovtunenko, Victor Anatolievich; Leugering, Günter (Eurasian Mathematical Journal, 2016)
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.