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.
Accepté le :
DOI : 10.1051/cocv/2018011
Mots-clés : Gradient flows, energy-dissipation principle, evolutionary Gamma convergence, quasistationary states, well-prepared initial conditions
@article{COCV_2019__25__A22_0,
author = {Schlichting, Andr\'e},
title = {Macroscopic limit of the {Becker{\textendash}D\"oring} equation via gradient flows},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018011},
mrnumber = {3986360},
zbl = {1440.49013},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2018011/}
}
TY - JOUR AU - Schlichting, André TI - Macroscopic limit of the Becker–Döring equation via gradient flows JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2018011/ DO - 10.1051/cocv/2018011 LA - en ID - COCV_2019__25__A22_0 ER -
%0 Journal Article %A Schlichting, André %T Macroscopic limit of the Becker–Döring equation via gradient flows %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2018011/ %R 10.1051/cocv/2018011 %G en %F COCV_2019__25__A22_0
Schlichting, André. Macroscopic limit of the Becker–Döring equation via gradient flows. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 22. doi : 10.1051/cocv/2018011. http://www.numdam.org/articles/10.1051/cocv/2018011/
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