Povstenko Yuriy, Ostoja-Starzewski Martin
Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
Department of Mechanical Science and Engineering, Beckman Institute and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Acta Mech. 2021 Feb;232(2):725-740. doi: 10.1007/s00707-020-02860-y. Epub 2020 Nov 30.
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.
研究了在线和半直线域上具有移动时谐源的温度的卡塔内奥电报方程。使用了拉普拉斯变换和傅里叶变换。得到了显示波前并阐明多普勒效应的表达式。研究了所考虑问题的几个特殊情况，包括热传导方程和波动方程。还研究了非移动时谐源和温度时谐边界条件下的准稳态解。
