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On a class of similarity solutions of the porous media equation. II. (English) Zbl 0365.35029


MSC:

35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
76S05 Flows in porous media; filtration; seepage
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[1] Ames, W. F., Nonlinear Partial Differential Equations in Engineering (1965), Academic Press: Academic Press New York · Zbl 0255.35001
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[9] Gilding, B. H.; Peletier, L. A., On a class of similarity solutions of the porous equation, J. Math. Anal. Appl., 55, 351-364 (1976) · Zbl 0356.35049
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[12] Lee, C. F., On the existence of solutions of a nonlinear differential diffusion system, (Proc. Roy. Edinburgh Sect. A, 71 (1972)), 1-7 · Zbl 0333.34010
[13] Marshak, R. E., Effect of radiation on shock wave behaviour, Phys. Fluids, 1, 24-29 (1958) · Zbl 0081.41601
[14] 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
[15] Shampine, L. F., Concentration-dependent diffusion, Quart. Appl. Math., 30, 441-452 (1973) · Zbl 0276.76044
[16] Shampine, L. F., Concentration-dependent diffusion II. Singular problems, Quart. Appl. Math., 31, 287-293 (1973) · Zbl 0278.76036
[17] 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
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