The geometry of dissipative evolution equations: the porous medium equation
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Submission date: 23. Jan. 1999
published in: Communications in partial differential equations, 26 (2001) 1-2, p. 101-174
DOI number (of the published article): 10.1081/PDE-100002243
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We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behaviour can be easily understood in this framework. We use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.