Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture
Analysis and PDE
Mathematical Sciences Publishers
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Cañizo, J., Einav, A., & Lods, B. (2017). Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture. Analysis and PDE, 10 (7), 1663-1708. https://doi.org/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.
Becker–Döring, nucleation, exponential convergence, entropy method
JAC was supported by the Marie-Curie CIG grant KineticCF and the Spanish Ministerio de Econom´ıa y Competitividad / European Regional Development Fund (ERDF/FEDER), project MTM2014-52056-P. AE was supported by EPSRC grant EP/L002302/1. BL acknowledges support of the de Castro Statistics Initiative, Collegio C. Alberto, Moncalieri, Italy.
External DOI: https://doi.org/10.2140/apde.2017.10.1663
This record's URL: https://www.repository.cam.ac.uk/handle/1810/266721