UBC DG + MP + PDE Seminar: Geuntaek Seo
- Date: 01/17/2023
- Time: 15:30
Lecturer(s):
Geuntaek Seo, Yonsei University
Location:
University of British Columbia
Topic:
A gradient flow for the Porous Medium Equations with Dirichlet boundary condition
Description:
In this talk, we consider the gradient flow structure of the porous medium equations with nonnegative constant boundary conditions. We prove that weak solutions to the equations can be obtained by the variational steepest descent scheme by considering an entropy functional with respect to Wb2 distance, which is a modified Wasserstein distance introduced by Figalli and Gigli [J. Math. Pures Appl. 94, (2010), pp. 107-130]. In addition, we establish an energy dissipation inequality. This is a joint work with Dongkwang Kim (Yonsei) and Dowan Koo (Yonsei).
Other Information: