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From Becker-Döring to Lifshitz-Slyozov: deriving the non-local boundary condition of a non-linear transport equation

Abstract : 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.
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Romain Yvinec, Julien Deschamps, Erwan Hingant. From Becker-Döring to Lifshitz-Slyozov: deriving the non-local boundary condition of a non-linear transport equation. Workshop on Multiscale and Hybrid Modelling in Cell and Cell Population Biology, Université Pierre et Marie Curie - Paris 6 (UPMC). Paris, FRA., Mar 2015, Paris, France. ⟨10.1051/itmconf/20150500017⟩. ⟨hal-02741964⟩

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