Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver

2013 ◽  
Vol 249 ◽  
pp. 1-12 ◽  
Author(s):  
A. Abubakar ◽  
T.M. Habashy
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Acoustic Modeling ◽  
Iterative Solver

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

scholarly journals Non-local problem with integral conditions for the three-dimensional high order hyperbolic equations

2020 ◽  
pp. 51-62
Author(s):  
Ш.Ш. Юсубов
Keyword(s):  
Integral Equation ◽  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
High Order ◽  
Mixed Derivative ◽  
Local Problem ◽  
Integral Conditions ◽  
Order Hyperbolic Equation ◽  
Non Local

В работе для трехмерного гиперболического уравнения высокого порядка с доминирующей смешанной производной исследуется разрешимость нелокальной задачи с интегральными условиями. Поставленная задача сводится к интегральному уравнению и с помощью априорных оценок доказывается существование единственного решения. In the work the solvability of the non-local problem with integral conditions is investigated for the three-dimensional high order hyperbolic equation with dominated mixed derivative. The problem is reduced to the integral equation and existence of the solution is proved by the help of aprior estimations.

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