Volume 25, 2019
|Number of page(s)||36|
|Published online||26 July 2019|
Macroscopic limit of the Becker–Döring equation via gradient flows
Institut für Angewandte Mathematik, Universität Bonn,
* Corresponding author: Schlichting@iam.uni-bonn.de
Accepted: 25 January 2018
This work considers gradient structures for the Becker–Döring equation and its macroscopic limits. The result of Niethammer [J. Nonlinear Sci. 13 (2003) 115–122] is extended to prove the convergence not only for solutions of the Becker–Döring equation towards the Lifshitz–Slyozov–Wagner equation of coarsening, but also the convergence of the associated gradient structures. We establish the gradient structure of the nonlocal coarsening equation rigorously and show continuous dependence on the initial data within this framework. Further, on the considered time scale the small cluster distribution of the Becker–Döring equation follows a quasistationary distribution dictated by the monomer concentration.
Mathematics Subject Classification: 49J40 / 34A34 / 35L65 / 49J45 / 49K15 / 60J27 / 82C26
Key words: Gradient flows / energy-dissipation principle / evolutionary Gamma convergence / quasistationary states / well-prepared initial conditions
© EDP Sciences, SMAI 2019
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