Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] K. Beckurtz and K. Wirtz, Neutron Physics, Springer-Verlag, New York, 1964
  • [2] D. Bogy and P. Naghdi, On heat conduction and wave propagation in rigid solids, Jour. of Math. Phys. 11, 917-923 (1970)
  • [3] J. Breezel and E. Nolan, Non-Fourier effects in the transmission of heat, Proc. 6th Conf. on Thermal Conductivity, Dayton, 237-254, October 1966
  • [4] J. Brown, D. Chung, and P. Matthews, Heat pulses at low temperature, Phys. Letters 21 , 241-243 (1966)
  • [5] C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 3-21 (1948/49) MR 0032898
  • [6] M. Chester, Second sound in solids, Phys. Rev. 131, 2013-2015 (1963)
  • [7] L. DeSocio and G. Gualtieri, A hyperbolic Stefan problem, Quart. Appl. Math. 41, 253-259 (1983) MR 719509
  • [8] M. Gurtin and A. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rat. Mech. Anal. 31, 113-126 (1968) MR 1553521
  • [9] J. C. Maxwell, On the dynamical theory of gases, Phil Trans. Royal Society London 157, 49-88 (1867)
  • [10] P. Morse and H. Feshback, Methods of Theoretical Physics, McGraw-Hill, New York, p. 865, 1953
  • [11] M. Sadd and J. Didlake, Non-Fourier melting of a semi-infinite solid, Jour. of Heat Transfer 99, 25-28 (1977)
  • [12] A. Solomon, V. Alexiades, D. Wilson, and J. Drake, The formulation of a hyperbolic Stefan problem, Quart. Appl. Math., to appear MR 814228
  • [13] A. Solomon, V. Alexiades, D. Wilson, and J. Greenberg, A hyperbolic Stefan problem with discontinuous temperature, to appear
  • [14] P. Vernotte, Les paradoxes de la théorie continue de l'equation de la chaleur, Comp. Rend. 246, 3154-3155 (1958) MR 0095679

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35R35, 35L99, 80A20

Retrieve articles in all journals with MSC: 35R35, 35L99, 80A20

Additional Information

DOI: https://doi.org/10.1090/qam/917025
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society