On inverse problem for a system of equations of elasticity theory

2002 ◽  
Vol 10 (2) ◽  
Author(s):  
Yu.E. Anikonov ◽  
M. Yamomoto
Keyword(s):  
Inverse Problem ◽  
Elasticity Theory ◽  
System Of Equations

scholarly journals Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 910
Author(s):  
Andrey Kovtanyuk ◽  
Alexander Chebotarev ◽  
Varvara Turova ◽  
Irina Sidorenko ◽  
Renée Lampe
Keyword(s):  
Inverse Problem ◽  
Oxygen Transport ◽  
Model Parameters ◽  
Cerebral Oxygen ◽  
System Of Equations ◽  
Blood Oxygen ◽  
Stationary Model ◽  
Average Oxygen Concentration ◽  
The Right ◽  
The Brain

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.

DEFINITION OF HYDRAULIC RESISTANCE OF UNDERGROUND OIL PIPELINE

2020 ◽  
Vol 69 (1) ◽  
pp. 56-61
Author(s):  
L. Yermekkyzy ◽  
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Numerical Method ◽  
Hydraulic Resistance ◽  
High Viscosity ◽  
System Of Equations ◽  
Oil Viscosity ◽  
Oil Pipeline ◽  
Conservation Of Momentum ◽  
Definition Of

The results of solving the inverse problem of determining the hydraulic resistance of a main oil pipeline are presented. The formulation of the inverse problem is formulated, a numerical method for solving the system of equations is described. The hydraulic resistance of the pipeline during the "hot" pumping of high-curing and high-viscosity oil changes during operation. Oil temperature decreases along the length of the pipeline due to heat transfer from the soil, leading to an increase in oil viscosity and an increase in hydraulic resistance.The dependence of the hydraulic resistance of the pipeline on the parameters of oil pumping is determined by solving the inverse problem. The inverse problem statement consists of a system of equations of laws of conservation of momentum, mass, energy and hydraulic resistance in the form of Altshul with unknown coefficients. The system of partial differential equations of hyperbolic type for speed and pressure is solved by the numerical method of characteristics, and the heat transfer equations by the iterative method of running counting.

Identification of the cancer ablation parameters during RF hyperthermia using gradient, evolutionary and hybrid algorithms

2017 ◽  
Vol 27 (3) ◽  
pp. 674-697 ◽  
Author(s):  
Marek Paruch
Keyword(s):  
Inverse Problem ◽  
Temperature Field ◽  
Electric Field ◽  
Electric Potential ◽  
Biological Tissue ◽  
Transfer Problem ◽  
Biological Tissues ◽  
Bioheat Transfer ◽  
System Of Equations ◽  
Content Type

Purpose The purpose of this study is to show that the methods of the numerical simulation can be a very effective tool for a proper choice of control parameters of artificial hyperthermia. An electromagnetic field induced by two external electrodes and a temperature field resulting from electrodes action in a 3D domain of biological tissue is considered. An important problem is the appropriate directing of heat in the region of tumor, so as to avoid damaging healthy cells surrounding the tumor. Recently, to concentrate the heat on the tumor, magnetic nanoparticles, which are introduced into the tumor, were used. The nanoparticles should be made of material that ensures appropriate magnetic properties and has a high biocompatibility with the biological tissue. External electric field causes the heat generation in the tissue domain. Design/methodology/approach The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes’ system of equations. These problems are coupled by source function being the additional component in the Pennes’ equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues. Findings The aim of investigations is to determine an electric potential of external electrodes and the number of nanoparticles introduced to a tumor region to obtain the artificial hyperthermia state. The tests performed showed that the proposed tool to solve the inverse problem provides correct results. Research limitations/implications In the paper the steady state bioheat transfer problem is considered, so the thermal damage is a function of the temperature only. Therefore, the solution can be considered as the maximum ablation zone of cancer. Additionally, the choice of appropriate parameters will be affected on the position and shape of the tumor and the electrodes. Originality/value In the paper the inverse problem has been solved using the evolutionary algorithm, gradient method and hybrid algorithm which is a combination of the two previous.

Determination of eigenvalues and discontinuous eigenfunctions of the system of equations of elasticity theory

1994 ◽  
Vol 72 (2) ◽  
pp. 2998-3003
Author(s):  
V. V. Skopetskii ◽  
V. S. Deineka ◽  
O. A. Marchenko
Keyword(s):  
Elasticity Theory ◽  
System Of Equations

Inverse problem for Oskolkov's system of equations

2015 ◽  
Vol 40 (17) ◽  
pp. 6123-6126 ◽  
Author(s):  
Vladimir E. Fedorov ◽  
Natalia D. Ivanova
Keyword(s):  
Inverse Problem ◽  
System Of Equations

Inverse Problem of the Interval Linear System of Equations

Computing ◽  
1999 ◽  
Vol 63 (2) ◽  
pp. 185-200 ◽  
Author(s):  
N. P. Seif ◽  
M. A. Hassanein ◽  
A. S. Deif
Keyword(s):  
Inverse Problem ◽  
Linear System ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Interval Linear System ◽  
Interval Linear

ON ASYMPTOTIC PROPERTIES OF SOLUTIONS OF THE SYSTEM OF EQUATIONS OF ELASTICITY THEORY

1978 ◽  
Vol 33 (5) ◽  
pp. 197-198
Author(s):  
I Kopachek ◽  
O A Oleinik
Keyword(s):  
Elasticity Theory ◽  
Asymptotic Properties ◽  
System Of Equations

Cauchy problem for a system of equations of plane dynamic elasticity theory

1978 ◽  
Vol 14 (5) ◽  
pp. 513-518
Author(s):  
V. I. Delei ◽  
M. P. Lenyuk
Keyword(s):  
Cauchy Problem ◽  
Elasticity Theory ◽  
System Of Equations ◽  
Dynamic Elasticity
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