Journal
ANALYSIS & PDE
Volume 10, Issue 7, Pages 1663-1708Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2017.10.1663
Keywords
Becker-Doing; nucleation; exponential convergence; entropy method
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Funding
- Marie-Curie CIG grant KineticCF
- Spanish Ministerio de Economia y Competitividad/European Regional Development Fund (ERDF/FEDER) [MTM2014-52056-P]
- EPSRC [EP/L002302/1]
- de Castro Statistics Initiative, Collegio C. Alberto, Moncalieri, Italy
- Engineering and Physical Sciences Research Council [EP/L002302/1] Funding Source: researchfish
- EPSRC [EP/L002302/1] Funding Source: UKRI
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We investigate the rate of convergence to equilibrium for subcritical solutions to the Becker-Doring 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-Doring 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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