  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.
