Abstract. The hyperbolic heat transfer model is obtained by replacing the classical Fourier's law with the relaxation relation iq; + q = -kVT. The conditions are derived for the local existence and uniqueness of classical solutions for a 3-dimensional Stefan problem of hyperbolic heat transfer model where the temperature may sustain a jump across the phase change interface.1. Introduction. In this paper, we shall consider the phase-change model proposed by J. Greenberg in [4] for the hyperbolic heat transfer model (see also [15]). The new feature of the model is that instead of the usual assumption on the continuity of the temperature across the phase-change interface, it is assumed that the relaxation relation between the temperature gradient VT and the heat flux q be interpreted as a conservation law that should also be satisfied across the interface. Based upon this assumption, a hyperbolic Stefan problem in one-dimensional space was discussed in [4], In this paper, the 3-dimensional case will be considered by applying the theory of energy estimate for multi-dimensional hyperbolic boundary value problems.The classical mathematical model for heat transfer and diffusion phenomena is of parabolic type, based upon Fourier's law
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