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The porous medium equation. (English) Zbl 0626.76097
Nonlinear diffusion problems, Lect. 2nd 1985 Sess. C.I.M.E., Montecatini Terme/Italy 1985, Lect. Notes Math. 1224, 1-46 (1986).
[For the entire collection see Zbl 0595.00014.]
The paper contains eight lectures concerning the mathematical study of nonlinear diffusion mechanism; in particular the porous medium equation is considered. The author presents the principal results concerning the basic estimates, the regularity in d-dimensional flow and the asymptotic behaviour of the solutions, obtained in the past then years (including the result of the author) but in general without proof. The paper contains also nomerous references to the main sources.
Reviewer: G.Pasa

76S05 Flows in porous media; filtration; seepage
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations