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The Cauchy-Stefan problem. (English) Zbl 0506.73106


MSC:

74A15 Thermodynamics in solid mechanics
35K05 Heat equation
35R35 Free boundary problems for PDEs
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References:

[1] Riemann, G. F. B., Weber, H.: Die partiellen Differentialgleichungen der mathematischen Physik, Bd. 2, 5. Aufl. Braunschweig: 1912.
[2] Stefan, J.: Über einige Probleme der Theorie der Wärmeleitung. S.-B. Wien. Akad. Mat. Natur.98, 473-484 (1889). · JFM 21.1197.01
[3] Rubinstein, L. I.: The Stefan problem (English translation). (Transl. Math. Monog. 27.) Providence: Am. Math. Soc. 1971.
[4] Carslaw, H. S., Jaeger, J. C.: Conduction of heat in solids, 2nd ed. Oxford: Clarendon Press 1959. · Zbl 0029.37801
[5] Crank, J.: The mathematics of diffusion, 2nd ed. Oxford: Clarendon Press 1975. · Zbl 0071.41401
[6] Ruddle, R. W.: The solidification of castings. London: Inst. Metals 1957.
[7] Bankoff, S. G.: Heat conduction of diffusion with change of phase. Adv. Chem. Eng.5, 75-150 (1964). · doi:10.1016/S0065-2377(08)60007-1
[8] Muehlbauer, J. C., Sunderland, J. E.: Heat conduction with freezing or melting. Appl. Mech. Rev.18, 951-959 (1965).
[9] Tiller, W. A.: Principles of solidification. In: Arts and sciences of growing crystals (Gilman, J. J., ed.). New York: Wiley 1963.
[10] Boley, B. A.: Survey of recent developments in the fields of heat conduction in solids and thermo-elasticity. Nuclear Eng. Des.18, 377-399 (1972). · doi:10.1016/0029-5493(72)90109-4
[11] Ockendon, J. R., Hodgkins, W. R. (eds.). Moving boundary problems in heat flow and diffusion. Oxford: Clarendon Press 1975. · Zbl 0295.76064
[12] Wilson, D. G., Solomon, A. D., Boggs, P. T. (eds.): Moving boundary problems. New York: Academic Press 1978. · Zbl 0432.00011
[13] Tao, L. N.: The Stefan problem with arbitrary initial and boundary conditions. Quart. Appl. Math.36, 223-233 (1978). · Zbl 0396.76075
[14] Tao, L. N.: The analyticity of solutions of the Stefan problem. Arch. Rat. Mech. Anal.72, 285-301 (1980). · Zbl 0416.35017 · doi:10.1007/BF00281593
[15] Tao, L. N.: On free boundary problems with arbitrary initial and flux conditions. Z. Angew. Math. Phys.30, 416-426 (1979). · Zbl 0455.73100 · doi:10.1007/BF01588886
[16] Tao, L. N.: Free boundary problems with radiation boundary conditions. Quart. Appl. Math.37, 1-10 (1979). · Zbl 0399.35097
[17] Tao, L. N.: The exact solutions of some Stefan problems with arbitrary heat flux and initial conditions. J. Appl. Mech.48, 732-736 (1981). · Zbl 0474.76102 · doi:10.1115/1.3157724
[18] Widder, D. V.: The heat equation. New York: Academic Press 1975. · Zbl 0322.35041
[19] Tao, L. N.: On the material time derivative of arbitrary order. Quart. Appl. Math.36, 323-324 (1978). · Zbl 0385.76004
[20] Abramowitz, M., Stegun, I. A. (eds.): Handbook of mathematical functions, NBS AMS 55. Washington D.C.: U.S. Government Printing Office 1964. · Zbl 0171.38503
[21] Tao, L. N.: On solidification problems including the density jump at the moving boundary. Quart. J. Mech. Appl. Math.32, 175-185 (1979). · Zbl 0452.76078 · doi:10.1093/qjmam/32.2.175
[22] Tao, L. N.: Dynamics of growth or dissolution of a gas bubble. J. Chem. Phys.69, 4189-4194 (1978). · doi:10.1063/1.437099
[23] Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs, N. J.: Prentice-Hall 1964. · Zbl 0144.34903
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