A one-phase hyperbolic Stefan problem in multi-dimensional space

Abstract

The hyperbolic heat transfer model is obtained by replacing the classical Fourier’s law with the relaxation relation τ q → t + q → = − k ∇ T \tau \vec qt + \vec q = - k\nabla T . The sufficient and necessary conditions are derived for the local existence and uniqueness of classical solutions for multi- D {\text {D}} Stefan problem of hyperbolic heat transfer model where phase change is accompanied with delay of latent heat storage.