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

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 Kovács and Ván (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 in 1D in the framework of the linearized 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.