Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation

The phase-lagging equation (PLE) is a new heat conduction equation which is different from the traditional heat equation since there exists a time lag of the heat-flux vector, while the damped wave equation (DWE) is its first-order approximation. In this article, we study the difference between the solutions of the PLE and the DWE by investigating the solutions of a test problem. Results show that the level of the solution obtained by the PLE is smaller in magnitude than the one obtained by the DWE, and that the DWE is a good approximation to the PLE when the time lag is small.