Finite propagation speed for limited flux diffusion equations

We prove that the support of solutions of a limited flux diffusion equation known as a relativistic heat equation evolves at a constant speed, identified as the speed of light c. For that we construct entropy sub- and super-solutions which are fronts evolving at speed c and prove the corresponding comparison principle between entropy solutions and sub- and super-solutions, respectively. This enables us to prove the existence of discontinuity fronts moving at light's speed.