Identification of nonlinear coefficient in a transport equation

Considered a problem of identification a nonlinear coefficient in a first order PDE via final observation. The problem is stated as an optimal control problem and solved numerically. Implicit finite difference scheme is used for the approximation of the state equation. A space of control variables is approximated by a sequence of finite-dimensional spaces with increaing dimensions. Finite dimensional problems are solved by a gradient method and numerical results are presented

Iterative solution methods for variational inequalities with nonlinear main operator and constraints to gradient of solution

Convergence of the preconditioned Uzawa-type and Arrow-Hurwitz-type iterative methods for nonlinear finite dimensional constrained saddle point problems is investigated. The general results are applied to the finite element approximation of a variational inequality with nonlinear main operator and constraints to gradient of solution. © 2012 Pleiades Publishing, Ltd

Easily implementable iterative methods for variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution

© 2015, walter de gruyter gmbh. All rights reserved. New iterative solution methods are proposed for the finite element approximation of a class of variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution. Implementation of every iteration of these methods reduces to the solution of a system of linear equations and a set of two-dimensional minimization problems. Convergence is proved by the application of a general result on the convergence of the iterative methods for a nonlinear constrained saddle point problem

Explicit algorithms to solve a class of state constrained parabolic optimal control problems

© 2015 by Walter de Gruyter Berlin/Boston. We consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the finite difference approximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulae. Computational experiments confirm the theoretical results

Non-overlapping domain decomposition method for a variational inequality with gradient constraints

© Published under licence by IOP Publishing Ltd.Non-overlapping domain decomposition method is applied to a variational inequality with nonlinear diffusion-convection operator and gradient constraints. The method is based on the initial approximation of the problem and its subsequent splitting into subproblems. For the resulting constrained saddle point problem block relaxation-Uzawa iterative solution method is applied

A penalty approach to the numerical simulation of a constrained wave motion

The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|u|2-1)u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation process is the construction of a time discretization scheme preserving-in some sense-the energy conservation property of the continuous model. The stability properties of the above scheme are discussed. The authors discuss also the finite element approximation and the quasi-Newton solution of the nonlinear elliptic system obtained at each time step from the time discretization. The results of numerical experiments are presented; they show that for the constraint of the original wave problem to be accurately verified we need to use a small value of the penalty parameter

The stabilization of unstable detonation waves for the mixture of nitromethane/methanol

Mass velocity profiles of detonation waves in mixtures of nitromethane with acetone and methanol with added diethylenetriamine sensitizer were measured using a VISAR laser interferometer. It was found that even small, about 1%, concentrations of acetone and methanol, inert diluents, led to instability of the one-dimensional detonation front in nitromethane. The results of the experiment show that the use of the sensitizer is an effective method of flow stabilization and if the concentration of the inert diluent does not exceed 10%, the detonation front becomes stable with the addition of 1% diethylenetriamine. At a higher diluent concentration, the sensitizer does not suppress the instability but decreases the oscillation amplitude by several times. The addition of diethylenetriamine to the mixture has been found to increase the detonation velocity

Visualization of nanoconstructions with DNA-Aptamers for targeted molecules binding on the surface of screen-printed electrodes

Nanoconstructions of gold nanoparticles (NPs) obtained via pulsed laser ablation in liquid with DNA-aptamer specific to protein tumor marker were visualized on the surface of screen-printed electrode using scanning electron microscopy (SEM) and confocal laser scanning microscopy (CLSM). AuNPs/aptamer nanoconstuctions distribution on the solid surface was studied. More uniform coverage of the carbon electrode surface with the nanoconstuctions was showed in comparison with DNA-aptamer alone on the golden electrode surface. Targeted binding of the tumor marker molecules with the AuNPs/DNA-aptamer nanoconstuctions was approved