scholarly journals Spatial Analogues of Numerical Quasiconformal Mapping Methods for Solving Identification Problems in Anisotropic Media

2019 ◽  
pp. 19-20
Author(s):  
Mykhailo Boichura ◽  
Olha Michuta ◽  
Andrii Bomba
Keyword(s):  
Image Reconstruction ◽  
Differential Equations ◽  
Quasiconformal Mapping ◽  
Complex Analysis ◽  
A Priori ◽  
Anisotropic Media ◽  
Identification Problems ◽  
Stream Functions ◽  
Tomographic Data ◽  
Spatial Bodies

The approach to solving the gradient problems of image reconstruction of spatial bodies using applied quasipotential tomographic data that is based on numerical complex analysis methods is extended to cases of anisotropic media. Here the distribution of eigen-directions of the conductivity tensor is considered a priori known. We propose to identify the parameters of the corresponding quasiideal stream by the way of minimizing the functional of the sum of squares of residuals which constructed using differential equations in partial derivatives that relate the quasipotential of velocity and the spatially quasicomplex conjugated stream functions

scholarly journals On a method of image reconstruction of anisotropic media using applied quasipotential tomographic data

2019 ◽  
Vol 6 (2) ◽  
pp. 211-219
Author(s):  
A. Ya. Bomba ◽  
◽  
M. T. Kuzlo ◽  
O. R. Michuta ◽  
M. V. Boichura ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Anisotropic Media ◽  
Tomographic Data

scholarly journals Spatial Analogues of Numerical Quasiconformal Mapping Methods for Solving Problems of Bursts Parameters Identification

2020 ◽  
pp. 11-14
Author(s):  
Mykhailo Boichura
Keyword(s):  
Image Reconstruction ◽  
Quasiconformal Mapping ◽  
Numerical Experiments ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Parameters Identification ◽  
Dimensional Case ◽  
Flow Function ◽  
Flow Lines ◽  
Tomographic Data

An approach to solving the problem of image reconstruction based on applied quasipotential tomographic data in the three-dimensional case is developed. It is based on the synthesis of spatial analogues of numerical quasiconformal mapping methods and algorithm for identifying the parameters of local bursts of homogeneous materials using similar methods on the plane. The peculiarity of the corresponding algorithm is taking into account (for each of the appropriate injections) the presence of only equipotential lines (with given values of the flow function or distributions of local velocities on them) and flow lines (with known potential distributions on them) at the domain boundary. Numerical experiments of simulative restoration of the environment structure are carried out.

scholarly journals Numerical complex analysis method for solving identification problems with using applied quasipotential tomographic data

2017 ◽  
pp. 14-26
Author(s):  
Andriy Bomba ◽  
Mykhailo Boichura
Keyword(s):  
Complex Analysis ◽  
Homogeneous Medium ◽  
Parametric Identification ◽  
Identification Problem ◽  
Analysis Method ◽  
Identification Problems ◽  
Analysis Problem ◽  
Conductivity Distribution ◽  
Piecewise Homogeneous Medium ◽  
Tomographic Data

The article deals with the problem of identification parameters of a piecewise homogeneous medium with using the applied quasipotential tomographic data when the data about the conductivity coefficient is incomplete. The method of image reconstruction, according to which solving of the analysis problem is reduced to the using numerical quasiconformal mappings methods and the synthesis problem is reduced to the solution the parametric identification problem when all possible variants of the conductivity distribution is considered. The reconstructed image of the conductivity distribution inside the investigated object on the basis of performed numerical calculations is constructed. The received results were analyzed. The proposed approach to reconstruction slightly increases the total number of iterations in some cases, but significantly simplifies the intermediate iterative problems solving.

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

scholarly journals On the theory and practice of thin-walled structures

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tamaz Vashakmadze
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Complex Analysis ◽  
Theory And Practice ◽  
Linear Case ◽  
Wide Sense ◽  
Partial Differential ◽  
Thin Walled Structures ◽  
Thin Walled

Abstract The basic problem of satisfaction of boundary conditions is considered when the generalized stress vector is given on the surfaces of elastic plates and shells. This problem has so far remained open for both refined theories in a wide sense and hierarchic type models. In the linear case, it was formulated by I. N. Vekua for hierarchic models. In the nonlinear case, bending and compression-expansion processes do not split and in this context the exact structure is presented for the system of differential equations of von Kármán–Mindlin–Reisner (KMR) type, constructed without using a variety of ad hoc assumptions since one of the two relations of this system in the classical form is the compatibility condition, but not the equilibrium equation. In this paper, a unity mathematical theory is elaborated in both linear and nonlinear cases for anisotropic inhomogeneous elastic thin-walled structures. The theory approximately satisfies the corresponding system of partial differential equations and the boundary conditions on the surfaces of such structures. The problem is investigated and solved for hierarchic models too. The obtained results broaden the sphere of applications of complex analysis methods. The classical theory of finding a general solution of partial differential equations of complex analysis, which in the linear case was thoroughly developed in the works of Goursat, Weyl, Walsh, Bergman, Kolosov, Muskhelishvili, Bers, Vekua and others, is extended to the solution of basic nonlinear differential equations containing the nonlinear summand, which is a composition of Laplace and Monge–Ampére operators.

scholarly journals A priori bounds for degenerate and singular evolutionary partial integro-differential equations

2010 ◽  
Vol 73 (11) ◽  
pp. 3572-3585 ◽  
Author(s):  
Vicente Vergara ◽  
Rico Zacher
Keyword(s):  
Differential Equations ◽  
A Priori ◽  
A Priori Bounds
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