Qualitative methods for investigation of a mathematical model of belt conveyor nonlinear vibrations (Q2870371)

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.