Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation-Reference-Cited by-同舟云学术

Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation

Published:2020-12-09 Issue: Volume: Page:
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Container-title:Mathematical Theorems - Boundary Value Problems and Approximations
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Author:

Aigulim Bayegizova,Assiyat Dadayeva

Abstract

The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.

Publisher

IntechOpen

Link

http://www.intechopen.com/download/pdf/71708

Reference10 articles.

1. Vladimirov VS. Generalized Functions in Mathematical Physics. Moscow: Mir; 1978. p. 282

2. Alekseeva LA, Dildabaev SA, Zhanbyrbaev AB, Zakiryanova GK. Boundary integral equation method in two & three dimensional problems of elastodynamics. International Journal of Computational Mechanics. 1996;18(2):147-157

3. Alekseeva LA. Boundary element method of boundary value problems of elastodynamics by stationary running loads. International Journal of Engineering Analysis with Boundary Element. 1998;(11):37-44

4. Alekseeva LA. Singular boundary integral equations of boundary value problems of elastodynamics in the case of subsonic traveling loads. Differential Equations. 2010;46(4):512-519

5. Alexeyeva LA. Generalized solutions of non-stationary boundary value problems for Maxwell's equations. Journal of Computational Mathematics and Mathematical Physics. 2002;42(1):76-88