The Approximation of the Solution of Wave Problems by Spectral Expansions Connected with Elliptic Differential Operators
Keywords:
Spectral expansion, wave problem, elliptic differential operatorAbstract
The current research is devoted to the investigation of the spectral expansions of elliptic differential operators corresponding to singular distributions, which can be used to describe the vibration process made of thin elastic membrane stretched tightly over a circular frame. By using the property that deflection of the membrane during the motion remains small compared to the size of the membrane we have obtained the sufficient conditions for summability of the spectral expansions connected with wave problems on the regions of the rectangular type.