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07 05 IM Noticia CovidTítulo: Energy estimates and convergence of weak solutions of the porous medium equation

Palestrante: Adriana Neumann (UFRGS)
Data: 10/05/2021
Horário: 15:00h
Local: Transmissão online.

Confira AQUI o link para a transmissão.

Resumo: In this talk, we study the convergence in the strong sense, with respect to the L^2-norm, of the weak solution of the porous medium equation (for short PME) with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The limiting function solves the same equation with Neumann (resp. Dirichlet) boundary conditions when the parameter is taken to zero (resp. infinity).

The keystone to prove this convergence result is a sufficiently strong energy estimate to the weak solution of the PME with a type of Robin boundary conditions.
Our approach to obtaining it is to consider an underlying microscopic dynamics, given by an interacting particle system, whose space-time evolution of the density of particles is ruled by the solution of those equations. We called this microscopic dynamic by the porous medium model (PMM) with slow boundary. The relation between the PMM and PME is stated in the paper, through the hydrodynamic limit for the PMM with slow boundary.

It is a joint work with Patrícia Gonçalves (IST - Lisbon) and Renato De Paula (IST - Lisbon), see more HERE.

All the talks are held in English.

The videos of the online seminars held in 2020 are available at HERE

For the 2021 series, a few days after each meeting the video should be available HERE.