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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 47 Documents MSC: 35K55 Nonlinear parabolic equations 76S05 Flows in porous media; filtration; seepage PDF BibTeX XML Cite \textit{B. H. Gilding} and \textit{L. A. Peletier}, J. Math. Anal. Appl. 55, 351--364 (1976; Zbl 0356.35049) Full Text: DOI References: [1] Ames, W.F, Similarity for the nonlinear diffusion equation, I & EC fundamentals, 4, 72-76, (1965) [2] Atkinson, F.V; Peletier, L.A, Similarity profiles of flows through porous media, Arch. rational mech. anal., 42, 369-379, (1971) · Zbl 0249.35043 [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 [6] Barenblatt, G.I, On limiting self-similar motions in the theory of unsteady filtration of a gas in a porous medium and the theory of the boundary layer, Prikl. mat. meh., 18, 409-414, (1954) · Zbl 0059.20404 [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, () This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.