IJPAM: Volume 113, No. 4 (2017)

Title

GENERALIZED SOLUTION OF A BOUNDARY VALUE
PROBLEM UNDER POINT EXPOSURE
OF EXTERNAL FORCES

Authors

A. Kerimbekov$^1$, E.F. Abdyldaeva$^2$, U.E. Duyshenalieva$^3$
$^{1,2}$Kyrgyz-Russian Slavic University
Bishkek, KYRGYZSTAN
$^3$Talas State University
Talas, KYRGYZSTAN

Abstract

In the paper, we study a problem of constructing the generalized solutions of the boundary value problem with wave equation under point exposure of external forces, when the wave process is described by Fredholm integral-differential equation. We have developed an algorithm for constructing the generalized solution of the boundary value problem, which together with its generalized derivative are elements of a Hilbert space. Sufficient conditions for the existence of a unique generalized solution are found. The presence of an integral term in equation stipulate the construction of two types of approximations of the generalized solution of the boundary problem. We prove the convergence of these approximations to the solution of the boundary value problem.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 49K20
Key Words and Phrases: boundary value problem, generalized solution, resolvent, point exposure, approximation solution, convergence

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How to Cite?

DOI: 10.12732/ijpam.v113i4.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 87 - 101


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