Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations
type: Dataset
description: We prove that any subcritical solution to the Becker-D\"{o}ring equations converges exponentially fast to the unique steady state with same mass. Our convergence result is quantitative and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, for which several bounds are provided. This improves the known convergence result by Jabin & Niethammer (see ref. [14]). Our approach is based on a careful spectral analysis of the linearized Becker-Döring equation (which is new to our knowledge) in both a Hilbert setting and in certain weighted $\ell^1$ spaces. This spectral analysis is then combined with uniform exponential moment bounds of solutions in order to obtain a convergence result for the nonlinear equation.
issued: 2026-06-04T02:36:23.378649
language: en
modified: 2026-06-04T02:36:23.378656
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-mpmathematics-mathmathematical-physics-math-ph
keyword: physmphyphysics-physicsmathematical-physics-math-ph
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00757263

Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations
type: Distribution
format: HTML
issued: 2026-06-04T02:36:23.400605
modified: 2026-06-04T02:36:23.349111
access URL: https://hal.science/hal-00757263

test_moissonnage_selune
type: Agent