On the estimation of the eigenfunctions of biharmonic operator in closed domain
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 expansio...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2018
|
| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/22954/1/On%20the%20estimation%20of%20the%20eigenfunctions%20of%20biharmonic%20operator%20in%20closed%20domain.pdf |
| _version_ | 1825812365368623104 |
|---|---|
| author | Ahmedov, Anvarjon A. Siti Nor Aini, Mohd Aslam Ibragimov, Gafurjan |
| author_facet | Ahmedov, Anvarjon A. Siti Nor Aini, Mohd Aslam Ibragimov, Gafurjan |
| author_sort | Ahmedov, Anvarjon A. |
| collection | UMP |
| description | 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. |
| first_indexed | 2024-03-06T12:28:04Z |
| format | Conference or Workshop Item |
| id | UMPir22954 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T12:28:04Z |
| publishDate | 2018 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | UMPir229542019-06-11T06:29:39Z http://umpir.ump.edu.my/id/eprint/22954/ On the estimation of the eigenfunctions of biharmonic operator in closed domain Ahmedov, Anvarjon A. Siti Nor Aini, Mohd Aslam Ibragimov, Gafurjan QA Mathematics QC Physics 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. AIP Publishing 2018-06 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/22954/1/On%20the%20estimation%20of%20the%20eigenfunctions%20of%20biharmonic%20operator%20in%20closed%20domain.pdf 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 (Published) https://doi.org/10.1063/1.5041631 |
| spellingShingle | QA Mathematics QC Physics Ahmedov, Anvarjon A. Siti Nor Aini, Mohd Aslam Ibragimov, Gafurjan On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title | On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title_full | On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title_fullStr | On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title_full_unstemmed | On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title_short | On the estimation of the eigenfunctions of biharmonic operator in closed domain |
| title_sort | on the estimation of the eigenfunctions of biharmonic operator in closed domain |
| topic | QA Mathematics QC Physics |
| url | http://umpir.ump.edu.my/id/eprint/22954/1/On%20the%20estimation%20of%20the%20eigenfunctions%20of%20biharmonic%20operator%20in%20closed%20domain.pdf |
| work_keys_str_mv | AT ahmedovanvarjona ontheestimationoftheeigenfunctionsofbiharmonicoperatorincloseddomain AT sitinorainimohdaslam ontheestimationoftheeigenfunctionsofbiharmonicoperatorincloseddomain AT ibragimovgafurjan ontheestimationoftheeigenfunctionsofbiharmonicoperatorincloseddomain |