The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

Abdulkasim Akhmedov; Mohd Zuki Salleh; Abdumalik Rakhimov

doi:10.37934/arfmts.86.2.101106

Authors

Abdulkasim Akhmedov Faculty of Mathematics and Science, Paragon International University, No 8, St 315, Boeng Kak 1, Toul Kork, 12151, Phnom Penh, Cambodia
Mohd Zuki Salleh Pusat Sains Matematik, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia
Abdumalik Rakhimov Kulliyah of Engineering, International Islamic University of Malaysia, IIUM, 53100 Kuala Lumpur, Malaysia

DOI:

https://doi.org/10.37934/arfmts.86.2.101106

Keywords:

Spectral expansion, wave problem, elliptic differential operator

Abstract

In this research, we investigate the spectral expansions connected with elliptic differential operators in the space of singular distributions, which describes the vibration process made of thin elastic membrane stretched tightly over a circular frame. The sufficient conditions for summability of the spectral expansions connected with wave problems on the disk are obtained by taking into account that the deflection of the membrane during the motion remains small compared to the size of the membrane and for wave propagation problems, the disk is made of some thermally conductive material.

Author Biographies

Abdulkasim Akhmedov, Faculty of Mathematics and Science, Paragon International University, No 8, St 315, Boeng Kak 1, Toul Kork, 12151, Phnom Penh, Cambodia

aakhmedov@paragoniu.edu.kh

Mohd Zuki Salleh, Pusat Sains Matematik, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia

zuki@ump.edu.my

Abdumalik Rakhimov, Kulliyah of Engineering, International Islamic University of Malaysia, IIUM, 53100 Kuala Lumpur, Malaysia

abdumalik@iium.edu.my

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