Ciclo de Palestras em Biomatemática – 17/06/2016
Ciclo de Palestras em Biomatemática
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