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2017 Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture
José Cañizo, Amit Einav, Bertrand Lods
Anal. PDE 10(7): 1663-1708 (2017). DOI: 10.2140/apde.2017.10.1663


We investigate the rate of convergence to equilibrium for subcritical solutions to the Becker–Döring equations with physically relevant coagulation and fragmentation coefficients and mild assumptions on the given initial data. Using a discrete version of the log-Sobolev inequality with weights, we show that in the case where the coagulation coefficient grows linearly and the detailed balance coefficients are of typical form, one can obtain a linear functional inequality for the dissipation of the relative free energy. This results in showing Cercignani’s conjecture for the Becker–Döring equations and consequently in an exponential rate of convergence to equilibrium. We also show that for all other typical cases, one can obtain an “almost” Cercignani’s conjecture, which results in an algebraic rate of convergence to equilibrium.


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José Cañizo. Amit Einav. Bertrand Lods. "Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture." Anal. PDE 10 (7) 1663 - 1708, 2017.


Received: 24 December 2016; Revised: 28 March 2017; Accepted: 29 May 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1373.34021
MathSciNet: MR3683925
Digital Object Identifier: 10.2140/apde.2017.10.1663

Primary: 34D05 , 35Q82 , 82C05 , 82C40

Keywords: Becker–Döring , entropy method , exponential convergence , nucleation

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 7 • 2017
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