Abstract
UDC 537.84
DOI https://doi.org/10.52577/eom.2021.57.5.52
The propagation of an electric pulse in a finite interval is investigated in the case when the pulse is generated at the input of the interval and absorbed at the end of the interval. The pulse propagation is described by a hyperbolic equation with regard for dissipation. The pulse generation at the input is specified as a Heaviside function, and the absorption at the output is set by a permanent magnet. The model describes the propagation of disturbances with a finite speed. A formulation of the corresponding initial boundary value problem is given, for the solution of which the Laplace transform in time is applied in the case of arbitrary coefficients. An exact analytical solution in the Laplace image space was obtained, and other applications with the complete absorption are presented. A general solution is constructed, and the case of low dissipation is considered for some values of the coefficients characterizing real situations.
Keywords: pulse propagation, finite interval, hyperbolic equation, dissipation, finite velocity, Laplace transform, initial boundary value problem.