A 3-dimensional hyperbolic Stefan problem with discontinuous temperature

Li, De Ning

doi:10.1090/qam/1121688

A $3$-dimensional hyperbolic Stefan problem with discontinuous temperature

Author: De Ning Li
Journal: Quart. Appl. Math. 49 (1991), 577-589
MSC: Primary 80A22; Secondary 35R35
DOI: https://doi.org/10.1090/qam/1121688
MathSciNet review: MR1121688
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Abstract: The hyperbolic heat transfer model is obtained by replacing the classical Fourier’s law with the relaxation relation $\tau {q_t} + q = - k\nabla T$. 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.

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