THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION

@article{Otto2001THEGO,
  title={THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION},
  author={Felix Otto},
  journal={Communications in Partial Differential Equations},
  year={2001},
  volume={26},
  pages={101 - 174}
}
  • F. Otto
  • Published 31 January 2001
  • Mathematics
  • Communications in Partial Differential Equations
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 that the time asymptotic behavior can be easily understood in this framework. We use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior. 
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