Hyperbolicity of the ballistic-conductive model of heat conduction: the reverse side of the coin

Abstract

The heat equation, based on Fourier's law, is commonly used for description of heat conduction. However, Fourier's law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short timescales, and at low temperatures. In the paper R. Kovacs and P. Van, Generalized heat conduction in heat pulse experiments, Int. J. Heat Mass Transf., 83:613-620, 2015, a ballistic-conductive (BC) model of heat conduction was developed. In this paper, we study the behavior of solutions to an initial value problem (IVP) in 1D in the framework of the linearized ballistic-conductive (BC) model. As a result of the study, an unphysical effect has been found when part of the initial thermal energy does not spread anywhere.