Convergence of the ‘relativistic’ heat equation to the heat equation as $c\to\infty$

Abstract

We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light $c$ tends to $\infty$ for any initial condition $u_0 \geq 0$ in $L^1(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)$.