23/05/2016 12:08

## Becker-Doring equations and its Lifschitz Slyozov limit, the entrant case

### Professor Erwan Hingant da UERJ

Segunda Palestra

Resumo: Becker-Doring equations is a phase transition model that describes aggregation and fragmentation of clusters by capturing or shedding monomers one-by-one. It consists in an infinite set of ordinary equation over each size \$i\geq 1\$ of clusters. We are interesting to link such system with a continuous model with continuous size \$x>0\$. Such limit model arise after scaling consideration and named Lifschitz-Slyozov. This consits in a non-linear transport equation. This equation is well-known when the flux at the boundary \$x=0\$ is negative, mnamely small clusters tends to fragment. In this presentation we are concerned with the opposite case, when small clusters tends to aggregate. We show our we can derive a boundary condition for the limit problem departing from the discrete version.
We would emphasis on 3 points: How a scaling procedure works; How can we prove a limit theorem; and introduce the notion of quasy steady state approximation for fast varying variable.

Dia – Horário: 17/06/2016 – 14:00-15:00
Local: Auditório do Departamento de Matemática (LAED), sala 007

E. Krukoski
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