Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations

Abstract

We prove that any subcritical solution to the Becker-Döring 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.

References in corpus (2)

• Celebrating Cercignani's conjecture for the Boltzmann equation
• Exhaustion of Nucleation in a Closed System

Cited by in corpus (9)

• Factorization for non-symmetric operators and exponential H-theorem
• Temporal oscillations in Becker-Doering equations with atomization
• A non-local problem for the Fokker-Planck equation related to the Becker-Döring model
• Exponentially-tailed regularity and time asymptotic for the homogeneous Boltzmann equation
• Trend to Equilibrium for the Becker-Döring Equations: An Analogue of Cercignani's Conjecture
• Uniform moment propagation for the Becker-Döring equation
• Boundary value for a nonlinear transport equation emerging from a stochastic coagulation-fragmentation type model
• Cutoff estimates for the Becker-Döring equations
• Polynomial decay to equilibrium for the Becker-Döring equations