The geometry of dissipative evolution equations: The porous medium equation

Authors
Otto, F
Citation
F. Otto, The geometry of dissipative evolution equations: The porous medium equation, COMM PART D, 26(1-2), 2001, pp. 101-174
Citations number
45
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN journal
03605302 → ACNP
Volume
26
Issue
1-2
Year of publication
2001
Pages
101 - 174
Database
ISI
SICI code
0360-5302(2001)26:1-2<101:TGODEE>2.0.ZU;2-0
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 re ader that it is mathematically natural, we show that the time asymptotic be havior can be easily understood in this framework. We use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.