scholarly journals Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

2005 ◽  
Vol 2005 (1) ◽  
pp. 361409 ◽  
Author(s):  
V Kokilashvili ◽  
V Paatashvili ◽  
S Samko
Keyword(s):  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Cauchy Type ◽  
Cauchy Type Integrals

scholarly journals ABOUT THE APPROXIMATE SOLUTION OF THE USUAL AND GENERALIZED HILBERT BOUNDARY VALUE PROBLEMS FOR ANALYTICAL FUNCTIONS

2000 ◽  
Vol 5 (1) ◽  
pp. 119-126
Author(s):  
V. R. Kristalinskii
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Cauchy Type ◽  
Analytical Functions ◽  
Method Of Solution ◽  
Cauchy Type Integrals ◽  
Hilbert Boundary Value Problem

In this article the methods for obtaining the approximate solution of usual and generalized Hilbert boundary value problems are proposed. The method of solution of usual Hilbert boundary value problem is based on the theorem about the representation of the kernel of the corresponding integral equation by τ = t and on the earlier proposed method for the computation of the Cauchy‐type integrals. The method for approximate solution of the generalized boundary value problem is based on the method for computation of singular integral of the formproposed by the author. All methods are implemented with the Mathcad and Maple.

scholarly journals Generalized Analytic Functions in Higher Dimensions

2007 ◽  
Vol 14 (3) ◽  
pp. 581-595
Author(s):  
Wolfgang Tutschke
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Higher Dimensions ◽  
Partial Differential ◽  
Generalized Analytic Functions ◽  
Linear Partial Differential Equations ◽  
Weakly Singular

Abstract Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions. One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.

scholarly journals Stability of mathematical models of the main problems of the anisotropic theory of elasticity

2020 ◽  
Vol 30 (1) ◽  
pp. 112-124
Author(s):  
A.V. Yudenkov ◽  
A.M. Volodchenkov
Keyword(s):  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Research Result ◽  
Theory Of Elasticity ◽  
Boundary Problems ◽  
Main Research ◽  
Contour Shape ◽  
Variable Function ◽  
Anisotropic Bodies

The boundary problems of the complex-variable function theory are effectively used while investigating equilibrium of homogeneous elastic mediums. The most complicated systems of the boundary value problems correspond to the case when an elastic body exhibits anisotropic properties. Anisotropy of the medium results in the drift of boundary conditions of the function that in general disrupts analyticity of the functions of interest. The paper studies systems of the boundary value problems with drift for analytic vectors corresponding to the primal elastic problems (first, second and mixed problems). Systems of analytic vectors with drift are reduced to equivalent systems of Hilbert boundary value problems for analytic functions with weak singularity integrators. The obtained general solution of the primal boundary value problems for the anisotropic theory of elasticity allows us to check the above problems for stability with respect to perturbations of boundary value conditions and contour shape. The research is relevant as there is necessity to apply approximate numerical methods to the boundary value problems with drift. The main research result comes to be a proof of stability of the systems of the vector boundary value problems with drift for analytic functions on the Hölder space corresponding to the primal problems of the elastic theory for anisotropic bodies in the case of change in the boundary value conditions and contour shape.

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