scholarly journals Asymptotic optimal control over elliptic system with special characteristics

1998 ◽  
Vol 6 ◽  
pp. 42
Author(s):  
Yu.N. Gorgo
Keyword(s):  
Optimal Control ◽  
Elliptic System ◽  
Distributed Control ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Higher Derivative ◽  
Elementary Region ◽  
Asymptotic Optimal Control ◽  
Internal Sets ◽  
Optimal Distributed Control

We construct and substantiate the solution of two-dimensional problem of the optimal distributed control over elliptic system with small parameter at higher derivative in an elementary region - in a square. We assume that the characteristics of limit control coincide with part of region boundary, and the control is unbounded.We show that the solutions of this problem have increasing singularities on some internal sets and, therefore, that the problem is bisingular.

scholarly journals OPTIMAL CONTROL OF A TWO-DIMENSIONAL RICHARDS-KLUTE EQUATION

2019 ◽  
pp. 39-48
Author(s):  
Andrii Tymoshenko
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
External Pressure ◽  
Point Sources ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Initial State ◽  
Source Power ◽  
The Mathematical Model

This article demonstrates an approach to optimal control of humidity using point sources for the two-dimensional problem. The mathematical model is based on Richards-Klute equation. The desired humidity state at the last moment is set and the solution should reach it from the known initial state by optimal source power. The moisture is assumed incompressible, the temperature and external pressure are constant.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

scholarly journals Two-dimensional black holes in a higher derivative gravity and matrix model

2008 ◽  
Vol 794 (1-2) ◽  
pp. 28-45 ◽  
Author(s):  
Kwangho Hur ◽  
Seungjoon Hyun ◽  
Hongbin Kim ◽  
Sang-Heon Yi
Keyword(s):  
Black Holes ◽  
Matrix Model ◽  
Two Dimensional ◽  
Higher Derivative
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