Concentration-dependent diffusion
Author:
L. F. Shampine
Journal:
Quart. Appl. Math. 30 (1973), 441-452
MSC:
Primary 80.35
DOI:
https://doi.org/10.1090/qam/413785
MathSciNet review:
413785
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Additional Information
N. E. Friedmann, Quasilinear heat flow, Trans. ASME 80, 635–645 (1958)
- J. Crank, The mathematics of diffusion, 2nd ed., Clarendon Press, Oxford, 1975. MR 0359551
A. V. Luikov, Analytical heat diffusion theory, trans, ed. J. P. Hartnett, Academic Press, New York, 1968
- W. F. Ames, Nonlinear partial differential equations in engineering, Academic Press, New York-London, 1965. MR 0210342
- L. A. Peletier, Asymptotic behaviour of temperature profiles of a class of nonlinear heat conduction problems, Quart. J. Mech. Appl. Math. 23 (1970), 441–447. MR 276599, DOI https://doi.org/10.1093/qjmam/23.3.441
- Carl Seyferth, Die Eindeutigkeit von Lösungen der eindimensionalen Diffusionsgleichung mit konzentrationsabhängigem Diffusionskoeffizienten, Math. Nachr. 24 (1962), 13–32 (German). MR 161045, DOI https://doi.org/10.1002/mana.19620240103
J. H. Weiner, Transient heat conduction in multiphase media, British J. Appl. Phys. 6, 361–363 (1955)
- J. R. Philip, Numerical solution of equations of the diffusion type with diffusivity concentration-dependent, Trans. Faraday Soc. 51 (1955), 885–892. MR 71876
S. Prager, The calculation of diffusion coefficients from sorption data, J. Chem. Phys. 19, 537–541 (1951)
J. Crank and M. E. Henry, Diffusion in media with variable properties, Trans. Faraday Soc. 45, 636–650 (1949)
M. Nagumo, Ueber die Differentialgleichung $y” = f\left ( {x,y,y’} \right )$, Proc. Phys. Math. Soc. Japan, Ser. 3, 19, 861–866 (1937)
- Paul B. Bailey, Lawrence F. Shampine, and Paul E. Waltman, Nonlinear two point boundary value problems, Mathematics in Science and Engineering, Vol. 44, Academic Press, New York-London, 1968. MR 0230967
M. N. Ozisik, Boundary value problems of heat conduction, International Textbook Co., Scranton, Pennsylvania, 1968
M. R. Hopkins, Heat conduction in a medium having thermal properties depending on the temperature, Proc. Phys. Soc. 50, 703–706 (1938)
- R. E. Kidder, Unsteady flow of gas through a semi-infinite porous medium, J. Appl. Mech. 24 (1957), 329–332. MR 0092536
T. Andre-Talamon, Sur la diffusion non-linéaire de la chaleur, Int. J. Heat Mass Transfer 11, 1351–1357 (1968)
J. L. Hwang, On the calculation of diffusion coefficients from sorption data, J. Chem. Phys. 20, 1320–1323 (1952)
M. Culter and G. T. Cheney, Heat wave method for the measurement of thermal diffusivity, J. Appl. Phys. 34, 1902–1909 (1963)
- T. J. Dekker, Finding a zero by means of successive linear interpolation, Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967) Wiley-Interscience, New York, 1969, pp. 37–48. MR 0256551
N. E. Friedmann, Quasilinear heat flow, Trans. ASME 80, 635–645 (1958)
J. Crank, The mathematics of diffusion, Oxford Univ. Press, London, 1970
A. V. Luikov, Analytical heat diffusion theory, trans, ed. J. P. Hartnett, Academic Press, New York, 1968
W. F. Ames, Nonlinear partial differential equations in engineering, Academic Press, New York, 1965
L. A. Peletier, Asymptotic behavior of temperature profiles of a class of non-linear heat conduction problems, Quart. J. Mech. Appl. Math 23, 441–447 (1970)
C. Seyferth, Die Eindeutigkeit von Lösungen der eindimensionalen Diffusionsgleichung mit konzentrationsabhängigem Diffusionskoeffizienten, Math. Nachr. 24, 13–32 (1962)
J. H. Weiner, Transient heat conduction in multiphase media, British J. Appl. Phys. 6, 361–363 (1955)
J. R. Philip, Numerical solution of equations of the diffusion type with diffusivity concentration-dependent, Trans. Faraday Soc. 51, 885–892 (1955)
S. Prager, The calculation of diffusion coefficients from sorption data, J. Chem. Phys. 19, 537–541 (1951)
J. Crank and M. E. Henry, Diffusion in media with variable properties, Trans. Faraday Soc. 45, 636–650 (1949)
M. Nagumo, Ueber die Differentialgleichung $y” = f\left ( {x,y,y’} \right )$, Proc. Phys. Math. Soc. Japan, Ser. 3, 19, 861–866 (1937)
P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear two point boundary value problems, Academic Press, New York, 1968
M. N. Ozisik, Boundary value problems of heat conduction, International Textbook Co., Scranton, Pennsylvania, 1968
M. R. Hopkins, Heat conduction in a medium having thermal properties depending on the temperature, Proc. Phys. Soc. 50, 703–706 (1938)
R. E. Kidder, Unsteady flow of gas through a semi-infinite porous medium, J. Appl. Mech. 27, 329–332 (1957)
T. Andre-Talamon, Sur la diffusion non-linéaire de la chaleur, Int. J. Heat Mass Transfer 11, 1351–1357 (1968)
J. L. Hwang, On the calculation of diffusion coefficients from sorption data, J. Chem. Phys. 20, 1320–1323 (1952)
M. Culter and G. T. Cheney, Heat wave method for the measurement of thermal diffusivity, J. Appl. Phys. 34, 1902–1909 (1963)
T. J. Dekker, Finding a zero by means of successive linear interpolation, in Constructive aspects of the the fundamental theorem of algebra, B. Dejon and P. Henrici, eds., Wiley, New York, 1969
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© Copyright 1973
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