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Mathematics Department Técnico Técnico

LisMath Seminar  RSS

11/10/2017, 17:00 — 18:00 — Room P9, Mathematics Building
Renato Ricardo de Paula, Universidade de Lisboa

Porous medium model in contact with slow reservoirs

This seminar is dedicated to the study of the porous medium model with slow reservoirs and to, heuristically, obtain the hydrodynamic equations for this model, depending on the parameter that rules the slowness of the reservoirs. The slow boundary means that particles can be born or die only at the boundary with rate proportional to $N^{-\theta}$, where $\theta \geq 0$ and $N$ is the scale parameter, while in the bulk the particle's exchange rate is either equal to $1$ or $2$, depending on the local configuration of the system. So, the goal is to explain how we can study the hydrodynamic limit of this interacting particle system, which guarantees that the evolution of the density of particles of this model is described by the weak solution of the corresponding hydrodynamic equation, namely, the porous medium equation with Dirichlet boundary conditions (when $\theta \in [0,1)$), with Robin boundary conditions (when $\theta = 1$) and Neumann boundary conditions (when $\theta \in (1, \infty)$). This presentation is based on the methods initially proposed in [3] and which are adapted to slow boundaries in [1] and [2].

Bibliography

[1] Bernardin, C.; Gonçalves, P; Oviedo, B.: Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps. https://arxiv.org/abs/1702.07216 (2017).

[2] Baldasso, R.; Menezes, O.; Neuman, A.; Souza, R. R.: Exclusion process with slow boundary. https://arxiv.org/abs/1407.7918 (2016).

[3] Franco, T.; Gonçalves, P.; Neumann, A.: Hydrodynamical behavior of symmetric exclusion with slow bonds. Ann. Inst. H. Poincaré Probab. Statist. 49, 2 (2013), 402-427.

See also

LisMath-seminar-Renato de Paula.pdf

Começar

Universidade de Lisboa FCUL