Large deviations and variational approach to generalized gradient flows

par Hong DUONG (Imperial College of London)

mardi 23 janv. 2018, 14:00 → 15:00 Europe/Paris

salle C 112 (UJM Campus Métare)

 "Large deviations and variational approach to generalized gradient flows"

 "In 1998, Jordan-Kinderlehrer-Otto (JKO) proved a remarkable result that the diffusion equation can be seen as a gradient flow of the Boltzmann entropy with respect to the Wasserstein distance. This result has sparked a large body of research in the field of partial differential equations and others in the last two decades. Many evolution equations have been proved to have a Wasserstein gradient flow structure such as the convection and nonlinear diffusion, the Cahn-Hilliard equation, the thin-film equation and finite Markov chains, just to name a few. Not only revealing physical nature of a PDE, a Wasserstein gradient flow structure can also be exploited to prove its well-posedness, to characterise long-time behaviour and to construct efficient computational methods.  However, the Wasserstein gradient flow theory is only applicable to dissipative systems.

In this talk, I will show how the JKO-scheme can be extended to non-dissipative systems and how these macroscopic schemes can be interpreted microscopically via the theory of large-deviations. In addition, I will also discuss about applications of this microscopic-macroscopic connection to multi-scale analysis of PDEs."