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On a class of similarity solutions of the porous media equation. (English) Zbl 0356.35049


MSC:

35K55 Nonlinear parabolic equations
76S05 Flows in porous media; filtration; seepage
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[1] Ames, W. F., Similarity for the nonlinear diffusion equation, I & EC Fundamentals, 4, 72-76 (1965)
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[4] Barenblatt, G. I., On some unsteady motions of a liquid an a gas in a porous medium, Prikl. Mat. Meh., 16, 67-78 (1952) · Zbl 0049.41902
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[10] Marshak, R. E., Effect of radiation on shock wave behaviour, Phys. Fluids, 1, 24-29 (1958) · Zbl 0081.41601
[11] Oleinik, O. A.; Kalashnikov, A. S.; Yui-Lin, Chzhou, The Cauchy problem and boundary problems for equations of the type of unsteady filtration, Izv. Akad. Nauk. SSSR Ser. Mat., 22, 667-704 (1958) · Zbl 0093.10302
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[13] Shampine, L. F., Concentration-dependent diffusion, Quart. Appl. Math., 30, 441-452 (1973) · Zbl 0276.76044
[14] Shampine, L. F., Concentration-dependent diffusion. II. Singular problems, Quart. Appl. Math., 31, 287-293 (1973) · Zbl 0278.76036
[15] Zel’dovich, Ya. B.; Kompaneets, A. S., On the theory of heat propagation for temperature-dependent thermal conductivity, (Collection Commemorating the Seventieth Birthday of Academician A. F. Ioffe (1950), Izdat. Akad. Nauk SSSR: Izdat. Akad. Nauk SSSR Moscow), 61-72
[16] Zel’dovich, Ya. B.; Raizer, Yu. P., (Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Vol. II (1967), Academic Press: Academic Press New York)
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