THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
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- 31 January 2001
- journal article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 26 (1-2) , 101-174
- https://doi.org/10.1081/pde-100002243
Abstract
We show that the porous medium equation has a gradient flowstructure which is both physically and mathematically natural. In orderto convince the reader that it is mathematically natural, we showthe time asymptotic behavior can be easily understood in this framework.We use the intuition and the calculus of Riemannian geometryto quantify this asymptotic behavior.Contents1 The porous medium equation as a gradient flow 21.1 The porous medium equation . . . . . . . . . . . . . . . . . ....Keywords
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