Abstract
The porous medium equation (PME)
is one of the simplest models of nonlinear diffusion equations. It arises naturally in the study of a number of problems describing the evolution of a continuous quantity subject to a nonlinear diffusion mechanism, which we can instance explain as caused by a diffusion coefficient of the form
if we write the PME as ut = div(c(u) ∇u). Among the applications of the PME have
-
(i)
Percolation of gas through porous media, where m ≥ 2 [M],
-
(ii)
Radiative heat transfer in ionized plasmas, where m ≃ 6 [ZR],
-
(iii)
Thin liquid films spreading under gravity, where m = 4 [Bu],
-
(iv)
Crowd-avoiding population spreading, where m>1 [GM].
Partly supported by USA-Spain Cooperation Agreement under Joint Research Grant CCB-8402023. The paper was written while the author was a member of the Institute for Mathematics and its Applications, University of Minnesota, 1985.
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Vazquez, J.L. (1987). Hyperbolic Aspects in the Theory of the Porous Medium Equation. In: Antman, S.S., Ericksen, J.L., Kinderlehrer, D., Müller, I. (eds) Metastability and Incompletely Posed Problems. The IMA Volumes in Mathematics and Its Applications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8704-6_20
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