Methods and Applications of Analysis

Volume 21 (2014)

Number 2

A note on existence and uniqueness of solutions for a thermodynamically consistent Becker-Döring model

Pages: 177 – 200

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n2.a1

Authors

Vincent Ssemaganda (Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Germany)

Gerald Warnecke (Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Germany)

Abstract

We study a thermodynamically consistent Becker-Döring model introduced by Dreyer and Duderstadt [J. Stat. Phys., 123, No. 1 (2006)]. In this model the fluxes have a possible singularity. We consider a more general model which accounts for the presence of an inert substance in a given system. We prove existence and uniqueness of solutions by using standard methods both for the original singular case and the extension to inert substances. Our results show that due to the structure of the model, solutions avoid the singularity if appropriate initial conditions are considered. We also study existence of equilibrium solutions. In some cases there is an upper bound on the mass contained in an equilibrium solution.

Keywords

nucleation, Becker-Döring model, kinetics of phase transition

2010 Mathematics Subject Classification

34A12, 34A34

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