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Gilding, B. H.; Peletier, L. A.

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

J. Math. Anal. Appl. 55, 351-364 (1976).
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Cited in 1 Review
Cited in 48 Documents

MSC:

35K55 Nonlinear parabolic equations
76S05 Flows in porous media; filtration; seepage
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\textit{B. H. Gilding} and \textit{L. A. Peletier}, J. Math. Anal. Appl. 55, 351--364 (1976; Zbl 0356.35049)
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References:

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[3] Atkinson, F.V; Peletier, L.A, Similarly solutions of the nonlinear diffusion equation, Arch. rational mech. anal., 54, 373-392, (1974) · Zbl 0293.35039
[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
[5] Barenblatt, G.I, On a class of exact solutions of the plane onedimensional problem of unsteady filtration into a porous medium, Prikl. mat. meh., 17, 739-742, (1953) · Zbl 0053.46103
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[7] Barenblatt, G.I; Zel’dovich, Ya.B, On the dipole-type solution in problems of unsteady gas filtration in the polytropic regime, Prikl. mat. meh., 21, 718-720, (1957)
[8] Hartman, P, Ordinary differential equations, (1964), John Wiley & Sons Inc New York · Zbl 0125.32102
[9] Kalashnikov, A.S; Kalashnikov, A.S, The occurrence of singularities in solutions of the nonsteady seepage equation, Z. vycisk. mat. i mat. fiz., USSR computational math. and math. phys., 7, 269-275, (1967), Translated as
[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
[12] Pattle, R.E, Diffusion from an instantaneous point source with concentrationdependent coefficient, Quart. J. mech. appl. math., 12, 407-409, (1959) · Zbl 0119.30505
[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, (), 61-72
[16] Zel’dovich, Ya.B; Raizer, Yu.P, ()
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