A coordinate transformation for the porous media equation that renders the free boundary stationary
Authors:
Morton E. Gurtin, Richard C. MacCamy and Eduardo A. Socolovsky
Journal:
Quart. Appl. Math. 42 (1984), 345-357
MSC:
Primary 35K65; Secondary 76S05
DOI:
https://doi.org/10.1090/qam/757173
MathSciNet review:
757173
Full-text PDF Free Access
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Additional Information
- L. A. Peletier, The porous media equation, Applications of nonlinear analysis in the physical sciences (Bielefeld, 1979), Surveys Reference Works Math., vol. 6, Pitman, Boston, Mass.-London, 1981, pp. 229–241. MR 659697
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A. S. Kalishnikov, On the occurrence of singularities in the solutions of the equation of nonstationary filtration, Vych. Mat. i Mat. Fis. 7, 440–444 (1967)
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E. DiBenedetto and D. C. Hoff, An interface tracking algorithm for the porous medium equation, Math. Res. Center, Univ. of Wisconsin, Tech. Summary Report 1489 (1983)
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M. Mimura and K. Tomoida, Numerical approximations for interface curves to a porous media equation (to appear)
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- D. G. Aronson, Regularity properties of flows through porous media: A counterexample, SIAM J. Appl. Math. 19 (1970), 299–307. MR 265774, DOI https://doi.org/10.1137/0119027
- Juan Luis Vázquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium, Trans. Amer. Math. Soc. 277 (1983), no. 2, 507–527. MR 694373, DOI https://doi.org/10.1090/S0002-9947-1983-0694373-7
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L. A. Peletier, The porous media equation, Application of Nonlinear Analysis in the Physical Sciences (eds. H. Amann, N. Bazley, K. Karchgassner), Pitman (1981), 229–241
O. A. Oleinik, A. S. Kalishnikov and Y.-L. Chzou, The Cauchy problem and boundary value problems for equations of the type of non-stationary filtration, Izv. Akad. Nauk SSR Ser. Mat. 22, 667–704 (1958)
A. S. Kalishnikov, On the occurrence of singularities in the solutions of the equation of nonstationary filtration, Vych. Mat. i Mat. Fis. 7, 440–444 (1967)
D. G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math. 17, 461–468 (1969)
---, Regularity properties of flows through porous media: the interface, Arch. Rat. Mech. Anal. 37, 1–10 (1970)
B. F. Knerr, The porous medium equation in one-dimension, Trans. Amer. Math. Soc. 234, 381–415 (1977)
E. DiBenedetto and D. C. Hoff, An interface tracking algorithm for the porous medium equation, Math. Res. Center, Univ. of Wisconsin, Tech. Summary Report 1489 (1983)
J. L. Gravelea and P. Jamet, A finite difference approach to some degenerate nonlinear parabolic equations, SIAM J. Appl. Math. 20, 199–223 (1971)
M. Mimura and K. Tomoida, Numerical approximations for interface curves to a porous media equation (to appear)
M. E. Gurtin, An introduction to continuum mechanics, Academic Press (1981)
D. G. Aronson, Regularity properties of flows through porous media: A counterexample, SIAM J. Appl. Math. 19, 299–207 (1970)
J. L. Vazquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of a gas in a porous medium, Trans. Amer. Math. Soc. 277, 507–528 (1983)
R. E. Pattle, Diffusion from an instantaneous point source with a concentration dependent coefficient, Quart. J. Mech. Appl. Math. 12, 407–409 (1959)
L. A. Caffarelli and A. Friedman, Regularity of the free boundary of a gas flow in an n-dimensional porous medium, Indiana Univ. Math. J. 29, 361–391 (1980)
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© Copyright 1984
American Mathematical Society