| Issue |
ITM Web of Conferences
Volume 5, 2015
Workshop on Multiscale and Hybrid Modelling in Cell and Cell Population Biology
|
|
|---|---|---|
| Article Number | 00017 | |
| Number of page(s) | 6 | |
| DOI | https://doi.org/10.1051/itmconf/20150500017 | |
| Published online | 11 December 2015 | |
From Becker-Döring to Lifshitz-Slyozov: deriving the non-local boundary condition of a non-linear transport equation
1 PRC INRA UMR85, CNRS, UMR7247, Université François Rabelais, IFCE, F-37380 Nouzilly, France
2 DIMA, Università degli Studi di Genova, Italy
3 Departamento de Matemática, Universidad Federal de Campina Grande, PB, Brasil
a e-mail: corresponding author: romain.yvinec@tours.inra.fr
b Funded by CAPES/IMPA from Brazil.
We investigate the connection between two classical models of phase transition phenomena, the (discrete size, Markov chain or infinite set of ODE) Becker-Döring equations and the (continuous size, PDE) Lifshitz-Slyozov equation. Contrary to previous studies, we use a weak topology that includes the boundary of the state space, allowing us to rigorously derive a boundary value for the Lifshitz-Slyozov model. This boundary condition depends on a particular scaling and is the result of a separation of time scales.
© Owned by the authors, published by EDP Sciences, 2015
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