Macroscopic limit of the Becker-Döring equation via gradient flows

Abstract

This work considers gradient structures for the Becker-Döring equation and its macroscopic limits. The result of Niethammer [17] 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.

References in corpus (3)

• Gradient flow structure for McKean-Vlasov equations on discrete spaces
• Trend to Equilibrium for the Becker-Döring Equations: An Analogue of Cercignani's Conjecture
• Quasi steady state approximation of the small clusters in Becker-Döring equations leads to boundary conditions in the Lifshitz-Slyozov limit

Cited by in corpus (3)

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• The Initial-boundary value problem for the Lifshitz-Slyozov equation with non-smooth rates at the boundary