Free boundary problems with radiation boundary conditions
Author:
L. N. Tao
Journal:
Quart. Appl. Math. 37 (1979), 1-10
MSC:
Primary 35C10; Secondary 35R35
DOI:
https://doi.org/10.1090/qam/530665
MathSciNet review:
530665
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Abstract: The paper is concerned with the free boundary problem of a semi-infinite body of arbitrarily prescribed initial temperature, subject to a mixed or radiation boundary condition at its face. The analytically exact solutions of temperature of both phases and the interfacial position are established in series of time and functions of the error integral family. Convergence of these series solutions is studied and proved. A few remarks on the solutions and their simplifications are then offered. A discussion on the analyticity of the solutions is also given. The paper concludes with an illustrative example, the so-called one-phase problem.
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S. G. Bankoff, Heat conduction or diffusion with change of phase, Adv. in Chem. Eng. 5, 75–150 (1964)
J. C. Muehbauer and J. E. Sunderland, Heat conduction with freezing or melting, Appl. Mech. Rev. 18, 951–959 (1965)
W. A. Tiller, Principles of solidification, in Arts and sciences of growing crystals, ed. J. J. Gilman, Wiley, New York, 1963
B. A, Boley, Survey of recent developments in the fields of heat conduction in solids and thermo-elasticity. Nuclear Eng. Des. 18, 377–399 (1972)
L. N. Tao, The Stefan problem with arbitrary initial and boundary conditions. Quart. Appl. Math. 36, 223–233 (1978)
L. N. Tao, On free boundary problems with arbitrary initial and flux conditions, to be published
D. V. Widder, The heat equation. Academic Press, New York, 1975
L. N. Tao, On the material time derivative of arbitrary order. Quart. Appl. Math. 36, 323–324 (1978)
C. Jordan, Calculus of finite differences, Chelsea, New York, 1965
A. Friedman, Free boundary problems for parabolic equations, I, Melting of solids, J. Math. Mech. 8, 499–517 (1959)
A. Friedman, Partial differential equations of parabolic type, Prentice Hall, Englewood Cliffs, N. J., 1964
J. R. Cannon and C. D. Hill, Existence, uniqueness, stability, and monotone dependence in a Stefan problem for the heat equation, J. Math. Mech. 17, 1–20 (1967)
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Article copyright:
© Copyright 1979
American Mathematical Society
