Two remarks on the stability of generalized hemivariational inequalities.
Two theorems on the Scorza Dragoni property for multifunctions
We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.
Two-dimensional examples of rank-one convex functions that are not quasiconvex
The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.
Two-dimensional Newton's problem of minimal resistance
Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions
Two-input control systems on the euclidean group SE (2)
Any two-input left-invariant control affine system of full rank, evolving on the Euclidean group SE (2), is (detached) feedback equivalent to one of three typical cases. In each case, we consider an optimal control problem which is then lifted, via the Pontryagin Maximum Principle, to a Hamiltonian system on the dual space 𝔰𝔢 (2)*. These reduced Hamilton − Poisson systems are the main topic of this paper. A qualitative analysis of each reduced system is performed. This analysis...
Two-level feedback control for interconnected distributed parameter systems of first order
Two-scale homogenization for a model in strain gradient plasticity
Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [J. Mech. Phys. Solids 52 (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.
Two-scale homogenization for a model in strain gradient plasticity
Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [J. Mech. Phys. Solids52 (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.
Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface
The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...
Tykhonov well-posedness of a heat transfer problem with unilateral constraints
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by . We associate to Problem an optimal control problem, denoted by . Then, using appropriate Tykhonov triples, governed by a nonlinear operator and a convex , we provide results concerning the well-posedness of problems...
Type-II singularities of two-convex immersed mean curvature flow
We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular...