This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic beha...

We show that finding a global optimal solution for the regularized Lq-minimization problem (q ≥ 1) is strongly NP-hard if the penalty function is concave but not linear in a neighborhood of zero and satisfies a very mild technical condition. This implies that it is impossible to have a fully polynomial-time approximation scheme (FPTAS) for such problems unless P = NP. This result clarifies the ...

Abstract We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in $${\mathbb {R}}^d$$ R d $$d\in \{2,3\}$$ ∈ { 2 , 3...

The aim of this paper is to derive spectral and condition number estimates of the single-layer operator for low-frequency multiple scattering problems. This work extends to dense media the analysis initiated in [7]. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary eleme...

Distributed sensing of structural states is essential to vibration control, health monitoring and shape control of precision structronic systems. Paraboloidal shells of revolution are widely used in aerospace, telecommunication, etc. structures. However, distributed sensing of paraboloidal shell structures is rarely investigated over the years. Micro-sensing characteristics, sensor segmentation...

Thin-walled structures like crash boxes may be used as energy absorption members in automotive chassis. There have been many studies addressing the behaviors of energy absorption members on frontal crash. These researches have attempted to predict the energy absorption and maximum impact load in shell structures. The energy absorption and maximum impact load depend on many parameters including ...

We consider a widely used higher order glacier flow model with a variety of parameterizations of wall slip, including Coulomb friction, regularized Coulomb friction laws and a power law. Mathematically, the Coulomb friction problem is found to be analogous to a classical friction problem in elasticity theory. We specifically analyze the case in which slip is possible everywhere at the boundary,...

We consider stability properties of discrete-time bilinear lters. Simple su cient conditions are given for bounded-input bounded-output stability (with not necessarily zero initial conditions), lp stability, and three other important types of stability. In particular, conditions are given under which asymptotically periodic inputs produce asymptotically periodic outputs with the same period. Re...

A Neumann boundary control problem for a second order elliptic state equation is considered which is regularized by an energy term which is equivalent to the H−1/2(Γ)-norm of the control. Both the unconstrained and the control constrained cases are investigated. The regularity of the state, control, and co-state variables is studied with particular focus on the singularities due to the corners ...

The immersed boundary (IB) method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid. In the continuous setting, the IB method couples an Eulerian description of the fluid to a Lagrangian description of the elastic structure via integral equations with Dirac delta function kernels, and in the discrete case, the d...