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Metastability and Incompletely Posed Problems
Volume 3 of the series The IMA Volumes in Mathematics and Its Applications pp 325342
Hyperbolic Aspects in the Theory of the Porous Medium Equation
 Juan Luis VazquezAffiliated withDivision de Matematicas, Universidad Autonoma
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 u_{t} = div(c(u) ∇u). Among the applications of the PME have
$$ {{\text{u}}_{\text{t}}} = \Delta ({{\text{u}}^{\text{m}}}),\,{\text{m>1}} $$
$$ {\text{c(u) = m}}{{\text{u}}^{{{\text{m  1}}}}} $$
(1.1)
 (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)
Crowdavoiding population spreading, where m>1 [GM].
 Title
 Hyperbolic Aspects in the Theory of the Porous Medium Equation
 Book Title
 Metastability and Incompletely Posed Problems
 Pages
 pp 325342
 Copyright
 1987
 DOI
 10.1007/9781461387046_20
 Print ISBN
 9781461387060
 Online ISBN
 9781461387046
 Series Title
 The IMA Volumes in Mathematics and Its Applications
 Series Volume
 3
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York
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 Editors

 Stuart S. Antman ^{(1)}
 J. L. Ericksen ^{(2)}
 David Kinderlehrer ^{(3)}
 Ingo Müller ^{(4)}
 Editor Affiliations

 1. Department of Mathematics, University of Maryland
 2. School of Mathematics and Department of Aerospace Engineering and Mechanics, University of Minnesota
 3. School of Mathematics, University of Minnesota
 4. FB9Hermann Föttinger Institut, Technical University
 Authors

 Juan Luis Vazquez ^{(5)}
 Author Affiliations

 5. Division de Matematicas, Universidad Autonoma, 28049, Madrid, Spain
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