[ABE-L] Próximo seminário (online) de probabilidade - IM-UFRJ 10 de maio -

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, *May 10, * from *3 p.m. to
4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminar is  https://meet.google.com/uew-ehhn-kby


Speaker:   *Adriana Neumann (UFRGS) *

Title: *Energy estimates and convergence of weak solutions of the  porous
medium equation*

Abstract: 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: https://link.springer.com/article/10.1007/s10955-020-02550-y,
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 in https://arxiv.org/abs/2101.08900.



All the talks are held in English.

The videos of the online seminars held in 2020 are available at
http://www.dme.ufrj.br/?page_id=2885

For the 2021 series, a few days after each meeting the video should be
available at http://www.dme.ufrj.br/?page_id=3027



Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares
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