Inverse Boundary Value Problem for Determination of Permittivity of Dielectric Body in a Waveguide using the Method of Volume Singular Integral Equation

2009 ◽  
Vol 129 (10) ◽  
pp. 675-680 ◽  
Author(s):  
Yury G. Smirnov
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Dielectric Body ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Volume Singular Integral Equation

Analysis of the Relaxation of Wall Electrons in a Plasma

1975 ◽  
Vol 30 (8) ◽  
pp. 937-946
Author(s):  
G. Ecker ◽  
K.-U. Riemann ◽  
A. Scholz
Keyword(s):  
Integral Equation ◽  
Kinetic Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Iteration Process ◽  
Standard Technique ◽  
Inelastic Collisions ◽  
Zeroth Order

Abstract A procedure is developed which renders the simultaneous description of angular and energy relaxation of wall electrons in a plasma possible. The plasma is assumed to be field free, allowance is made for elastic and inelastic collisions with neutrals, as well as for electron-electron encounters. The procedure is based on an expansion in terms of the eigenfunctions of a suitable part of the kinetic equation. In the zeroth order, the problem is reduced to a boundary value problem of the Sturm type, and subsequent solution of a singular integral equation by standard technique. To account for the rest of the kinetic equation, we construct a Green′s function which forms the basis for an iteration process. The application of the procedure is illustrated with an example.

scholarly journals Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity

2008 ◽  
Vol 2008 ◽  
pp. 1-27 ◽  
Author(s):  
A. V. Balakrishnan ◽  
M. A. Shubov
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Normal Velocity ◽  
Initial Boundary Value ◽  
Slender Wing

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet. We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work.

scholarly journals On a boundary value problem for the heat equation and a singular integral equation associated with it

2021 ◽  
Vol 399 ◽  
pp. 126009
Author(s):  
Meiramkul Amangaliyeva ◽  
Muvasharkhan Jenaliyev ◽  
Sagyndyk Iskakov ◽  
Murat Ramazanov
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Singular Integral ◽  
Boundary Value
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