Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

Effective Hamiltonains and degenerate perturbation theory calculations of the mass spectrum in lattice QCD

Hamiltonian quantum chromodynamics has been formulated on a discrete lattice, in an attempt to calculate the hadronspectrum using strong coupling expansions. Previous attempts have involved including an irrelevant four-fermion interaction term in the Hamiltonian. As well as making the quark content of the zeroth order states the same as that of the simple additive quark model, this term splits the infinite zeroth order degeneracies of the original Hamiltonian. In this paper we calculate the masses of low lying states in the absence of such a term, using an effective Hamiltonian method to solve the degeneracy problem. We discuss the problems of continuing our series to the continuum limit in the presence of level repulsion.     

V-Limit Analysis of Vector-Valued Mappings

For an arbitrary net of mappings defined on subsets of the Hausdorff space (X, ) and acting into a vector topological space (Y, ) semiordered by a solid cone , we introduce the notion of V-limit. We investigate topological and sequential properties of V-limit mappings and establish sufficient conditions for their existence. The results presented can be used as a basis for the procedure of averaging of problems of vector optimization.     

Moreau-yosida approximation of conditional minimization problems and its limit properties

For a family of conditional minimization problems we obtain a representation of its variational S-limits in terms of pointwise limits of Moreau-Yosida approximations. Bibliography: 4 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 62–69.     

Asymptotic Analysis of State Constrained Semilinear Optimal Control Problems

The asymptotic behavior of state-constrained semilinear optimal control problems for distributed-parameter systems with variable compact control zones is investigated. We derive conditions under which the limiting problems can be made explicit. We gratefully acknowledge the support of the DAAD. The paper was prepared during the visit of the first author at the Institute of Applied Mathematics II, University Erlangen-Nuremberg in 2003.     

On the state stability of a system of integro-differential equations of nonstationary aeroelasticity

We consider a process of nonstationary aeroelasticity, which is described by a system of integro-dijferential equations that cannot be solved for the derivative. We formulate necessary and sufficient conditions, in terms of Lyapunov functionals, for the exponential stability of such a system with respect to the metric of an infinite Hilbert space. A formula is given for the total derivative of a Lyapunov functional via the initial equations of motion.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 70, pp. 112–121, 1990.     

Photoelastic Properties of Potassium Sulfate Crystals

Physics of the Solid State - The spectral dependences of the absolute piezooptic coefficients of potassium sulfate crystals are studied. It is established that their dispersion dependence is...