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Blood Flow Imaging with Ultrafast Doppler
Published on: October 14, 2020
Doppler effect described by the solutions of the Cattaneo telegraph equation
Yuriy Povstenko1, Martin Ostoja-Starzewski2
1Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
Abstract:
The Cattaneo telegraph equation for temperature with moving time-harmonic source is studied on the line and the half-line domain. The Laplace and Fourier transforms are used. Expressions which show the wave fronts and elucidate the Doppler effect are obtained. Several particular cases of the considered problem including the heat conduction equation and the wave equation are investigated. The quasi-steady-state solutions are also examined for the case of non-moving time-harmonic source and time-harmonic boundary condition for temperature.
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