IJPAM: Volume 116, No. 4 (2017)

Title

THE APPLICATION OF THE METHOD OF
ENERGY INEQUALITIES FOR EQUATION OF BEAM

Authors

Akimov Andrey$^1$, A.A. Gimaltdinova$^2$
$^1$Bashkir State University
Sterlitamak Branch
Lenina Str., 47A, Sterlitamak, 453103
Republic of Bashkortostan, RUSSIA
$^{2}$Ufa State Petroleum Technological University
Kosmonavtov Str., 1, Ufa, 450062
Republic of Bashkortostan, RUSSIA

Abstract

In this paper it is shown that under specified conditions on the initial data a certain infinite coupled system of ordinary differential equations has a solution satisfying an auxiliary convergence condition. The infinite system discussed is essentially the Galerkin expansion of the solution to a given quasi-linear wave equation of forth order. The results obtained suffice to prove the existence of a solution to this equation of oscillations of a beam.

History

Received: 2017-08-19
Revised: 2017-11-01
Published: November 23, 2017

AMS Classification, Key Words

AMS Subject Classification: 35G31
Key Words and Phrases: quasi-linear wave equation, method of energy inequalities, equation of beam

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Bibliography

1
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2
P. Davis, A quasi-linear hyperbolic and related third order equation, J. Math, Anal. Appl., 51 (1975), 596-606, doi: https://doi.org/10.1016/0022-247X(75)90110-9.

3
A. Akimov, E. Safin, A. Agafonova, On uniqueness generalized problem of Tricomi for the Chaplygin equation, International Journal of Pure and Applied Mathematics, 115, No. 4 (2017), 895-899, doi: https://doi.org/10.12732/ijpam.v115i4.23.

4
A. Andrey, A. Alena, Analytical solutions for linear Volterra and Abel integral equations of second kind using a power series method, International Journal of Pure and Applied Mathematics, 105, No. 3 (2015), 529-535, doi: https://doi.org/10.12732/ijpam.v105i3.18.

How to Cite?

DOI: 10.12732/ijpam.v116i4.22 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: 116
Issue: 4
Pages: 1075 - 1080


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