A hyperbolic Stefan problem
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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J. Brown, D. Chung, and P. Matthews, Heat pulses at low temperature, Phys. Letters 21 , 241–243 (1966)
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A. Solomon, V. Alexiades, D. Wilson, and J. Greenberg, A hyperbolic Stefan problem with discontinuous temperature, to appear
- Pierre Vernotte, Les paradoxes de la théorie continue de l’équation de la chaleur, C. R. Acad. Sci. Paris 246 (1958), 3154–3155 (French). MR 95679
K. Beckurtz and K. Wirtz, Neutron Physics, Springer-Verlag, New York, 1964
D. Bogy and P. Naghdi, On heat conduction and wave propagation in rigid solids, Jour. of Math. Phys. 11, 917–923 (1970)
J. Breezel and E. Nolan, Non-Fourier effects in the transmission of heat, Proc. 6th Conf. on Thermal Conductivity, Dayton, 237–254, October 1966
J. Brown, D. Chung, and P. Matthews, Heat pulses at low temperature, Phys. Letters 21 , 241–243 (1966)
C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 3–21 (1948/49)
M. Chester, Second sound in solids, Phys. Rev. 131, 2013–2015 (1963)
L. DeSocio and G. Gualtieri, A hyperbolic Stefan problem, Quart. Appl. Math. 41, 253–259 (1983)
M. Gurtin and A. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rat. Mech. Anal. 31, 113–126 (1968)
J. C. Maxwell, On the dynamical theory of gases, Phil Trans. Royal Society London 157, 49–88 (1867)
P. Morse and H. Feshback, Methods of Theoretical Physics, McGraw-Hill, New York, p. 865, 1953
M. Sadd and J. Didlake, Non-Fourier melting of a semi-infinite solid, Jour. of Heat Transfer 99, 25–28 (1977)
A. Solomon, V. Alexiades, D. Wilson, and J. Drake, The formulation of a hyperbolic Stefan problem, Quart. Appl. Math., to appear
A. Solomon, V. Alexiades, D. Wilson, and J. Greenberg, A hyperbolic Stefan problem with discontinuous temperature, to appear
P. Vernotte, Les paradoxes de la théorie continue de l’equation de la chaleur, Comp. Rend. 246, 3154–3155 (1958)
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Article copyright:
© Copyright 1987
American Mathematical Society