A hyperbolic Stefan problem

Showalter, R. E.; Walkington, N. J.

doi:10.1090/qam/917025

Authors: R. E. Showalter and N. J. Walkington
Journal: Quart. Appl. Math. 45 (1987), 769-781
MSC: Primary 35R35; Secondary 35L99, 80A20
DOI: https://doi.org/10.1090/qam/917025
MathSciNet review: 917025
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Abstract: A free-boundary problem of Stefan type is presented under constitutive assumptions on flux and energy which contain an effective time delay. This contains the hyperbolic telegraphers equation and, hence, has the feature that propagation speed of disturbances is bounded. With the appropriate physically consistent condition on the interface this is shown to lead to a well-posed weak formulation of the problem.

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