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MiS Preprint
8/1999

The geometry of dissipative evolution equations: the porous medium equation

Felix Otto

Abstract

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.

Received:
Jan 23, 1999
Published:
Jan 23, 1999

Related publications

inJournal
2001 Repository Open Access
Felix Otto

The geometry of dissipative evolution equations: the porous medium equation

In: Communications in partial differential equations, 26 (2001) 1-2, pp. 101-174