Variational formulation for degenerate and nonlocal PDEs
Speaker: Asst. Prof. Dương Mạnh Hồng (Birmingham )

Thời gian: 14h ngày 18/06/2020

Hình thức: Online qua Google meet

Tóm tắt: In 1998, Jordan-Kinderleher-Otto (JKO) proved a remarkable result that the Fokker-Planck equation can be seen as a gradient flow of the Boltzmann entropy with respect to the Wasserstein distance. This result has sparked off a large body of research in the fields of partial differential equations, optimal transportation theory and probability theory over the last two decades. Many evolution equations have been proved to have a Wasserstein gradient flow structure such as the convection and nonlinear diffusion equation, the Cahn-Hilliard equation, the thin-film equation and finite Markov chains, just to name a few.

In this talk, I will present several extensions of the JKO approach to degenerate and nonlocal PDEs. If time permits, I will also discuss the Wasserstein barycenter problem, which has recently found many applications in statistics and image processing, and how this problem relates to the JKO-scheme for the time-fractional Fokker Planck equation.

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