×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ames, W.F, Nonlinear partial differential equations in engineering, (1965), Academic Press New York · Zbl 0255.35001
[2] Atkinson, F.V; Peletier, L.A, Similarity profiles of flows through porous media, Arch. rational mech. anal., 42, 363-379, (1971) · Zbl 0249.35043
[3] Atkinson, F.V; Peletier, L.A, Similarity 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 and 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 one-dimensional 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] Craven, A.H; Peletier, L.A, Similarity solutions for degenerate parabolic equations, J. math. anal. appl., 38, 73-81, (1972) · Zbl 0237.35043
[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
[10] Hartman, P, Ordinary differential equations, (1964), Wiley New York · Zbl 0125.32102
[11] Kalashnikov, A.S; Kalashnikov, A.S, The occurence of singularities in solutions of the non-steady seepage equation, Z. vycisl. mat. i mat. fiz., USSR comput. math. and math. phys., 7, 269-275, (1967), Translated as:
[12] Lee, C.F, On the existence of solutions of a nonlinear differential diffusion system, (), 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, (), 61-72
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.