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On the estimation of the eigenfunctions of biharmonic operator in closed domain

Ahmedov, Anvarjon A. and Siti Nor Aini, Mohd Aslam and Ibragimov, Gafurjan (2018) On the estimation of the eigenfunctions of biharmonic operator in closed domain. In: 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence (SKSM 2017), 27-29 August 2017 , Kuantan, Pahang. , 1974. ISSN 0094-243X

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Abstract

In the current research, the sufficient conditions for uniform convergence of the eigenfunction expansions of the biharmonic operator in closed domain are investigated. The problems which appear in the study of various vibrating systems are the reasons to develop the theory of eigenfunction expansions of the biharmonic operators. Because of the mathematical description of the physical processes taking place in real space are based on the spectral theory of differential operators, particularly biharmonic operator. The biharmonic equation is encountered in plane problems of elasticity. It is also used to describe slow flows of viscous incompressible fluids. In this paper the uniform estimations for eigenfunctions of biharmonic operator is obtained using the resolvent operator of the biharmonic equations. In the future works the obtained estimation will be used to prove uniform convergence of eigenfunction expansions of biharmonic operator in closed domain.

Item Type: Conference or Workshop Item (Lecture)
Additional Information: Indexed by SCOPUS & WOS
Uncontrolled Keywords: Biharmonic operator; Convergence; Eigenfunction expansions; Mean value
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Faculty/Division: Faculty of Industrial Sciences And Technology
Depositing User: Mrs. Neng Sury Sulaiman
Date Deposited: 11 Jun 2019 06:29
Last Modified: 11 Jun 2019 06:29
URI: http://umpir.ump.edu.my/id/eprint/22954
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