Behavior of the linearized ballistic-conductive model of heat conduction in three-dimensional space

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. As a replacement for Fourier's law, many models have been proposed within the framework of various theories. In this paper we study the behavior of solutions to an initial value problem in 3D in the framework of the linearized ballistic-conductive (BC) model. As a result, an unphysical effect is detected when the temperature in the heat wave takes negative values.