The Stefan problem for a hyperbolic heat equation

AbstractIn this paper we consider the 1-phase, 1-dimensional Stefan problem corresponding to the hyperbolic heat equation obtained by relaxing the Fourier law, taking τqt + q = −kθx where q is the flux, θ the temperature, k the conductivity, and τ > 0 the relaxation coefficient. We prove existence and uniqueness of a smooth solution with smooth free boundary. We also study the limiting solution as τ → 0, showing (under some conditions) that it converges to the solution of the classical Stefan problem