On the Solvability of Nonhomogeneous Boundary Value Problem for the Burgers Equation in the Angular Domain and Related Integral Equations

2017 ◽  
pp. 123-141
Author(s):  
Meiramkul M. Amangaliyeva ◽  
Muvasharkhan T. Jenaliyev ◽  
Minzilya T. Kosmakova ◽  
Murat I. Ramazanov
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Burgers Equation ◽  
Boundary Value ◽  
Angular Domain ◽  
Nonhomogeneous Boundary ◽  
Related Integral

scholarly journals A mixed boundary value problem of a cracked elastic medium under torsion

2021 ◽  
pp. 10-10
Author(s):  
Belkacem Kebli ◽  
Fateh Madani
Keyword(s):  
Boundary Value Problem ◽  
Elastic Medium ◽  
Integral Equations ◽  
Integral Transformation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Crack Problem ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack

The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.

scholarly journals On the Solution of the Exterior Boundary Value Problem with the Aid of Series

1978 ◽  
Vol 41 ◽  
pp. 175-176
Author(s):  
M. S. Petrovskaya
Keyword(s):  
Gravitational Field ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Integral Equations ◽  
Boundary Value ◽  
Parameter Method ◽  
Small Parameter Method ◽  
Exterior Boundary ◽  
Exterior Boundary Value Problem ◽  
Molodensky Problem

AbstractThe exterior gravitational field depending on the Earth’s non-sphericity is usually determined from the analysis of satellite data or by the solution of the exterior boundary value problem. In the latter case some integral equations are solved which correlate the exterior potential with the known vector of gravity and the shape of the Earth’s surface (molodensky problem). In order to carry out the integration the small parameter method is applied. As a result, all the quantities which involve the equations should be expanded in powers of a certain small parameter, among these being the heights of the Earth’s surface points as well as the inclination α of the Earth’s physical surface. Since the angle α can be significant, especially in mountains, and in fact does not depend on any small parameter then the solution of integral equations is possible only for the Earth’s surface which is smoothed enough.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

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