Hyperbolicity of the heat equation

In this manuscript, a comparison between the parabolic and hyperbolic partial differential equations for heat diffusion is studied. First, numerical results and an eigenvalue analysis for these two types of equations are shown, which help to understand the difference in the system dynamics. Then, both equations are also considered in a Stefan problem for the melting of an ice block in a one-dimensional setting. The results show that the hyperbolic partial differential equation shows a finite speed of propagation of heat and can represent the system as properly as the parabolic equation.