Qualitative methods for investigation of a mathematical model of belt conveyor nonlinear vibrations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1289.35013
author: P. Ya. Pukach
publication date: 2014-01-17T00:00:00Z
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 6247738
zbMATH Keywords: correctness conditions of problem solution
zbMATH Keywords: Galerkin method
MaRDI profile type: Publication
title: Qualitative methods for investigation of a mathematical model of belt conveyor nonlinear vibrations
published in: Matematychni Metody ta Fizyko-Mekhanichni Polya
review text: A technique for qualitative investigation of the solution to the mathematical model of belt conveyor vibrations is presented in terms of general approaches of nonlinear boundary value problems theory. To this end, the following equation is considered NEWLINE\[NEWLINE \frac{\partial^2u}{\partial t^2} - \frac{\partial}{\partial x}\bigg(a(x)\, \frac{\partial u}{\partial x}\bigg) + g(x)\, \bigg| \frac{\partial u}{\partial t}\bigg| ^{p-2} \frac{\partial u}{\partial t}=f(x,t),\qquad p>2,\tag{1} NEWLINE\]NEWLINE with the boundary conditions NEWLINE\[NEWLINE u(0,t)=u(\ell,t)=0.\tag{2} NEWLINE\]NEWLINE A case of the system being at the instant of time quite distant from the initial time is investigated. The technique based on the application of the monotony method and the Galerkin method allows the author to substantiate correctness of the model solution and enables him to apply various approximate methods for its investigation.
reviewed by: A. A. Martynyuk
description: scientific article; zbMATH DE number 6247738