The geometry of dissipative evolution equation

SIAM Student Seminar
Friday, March 5, 2010 - 1:00pm
1 hour (actually 50 minutes)
Skiles 255
Georgia Tech
Last semester, I reviewed the relation between dynamical system, Fokker-Planck equation and thermodynamics (free energy and Gibbs distribution). This time let's go further. I will review the geometric properties of a kind of dissipative evolution equations. I will explain why this kind of evolutionary equations (Fokker-Planck equation, nonlinear Fokker-Planck equation, Porous medium equation) are the gradient flow of some energy function on a Riemannian manifold -- 2-Wasserstein metric space.