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Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture

dc.creatorCañizo, JA
dc.creatorEinav, Amit
dc.creatorLods, B
dc.date.accessioned2017-05-29
dc.date.accessioned2018-11-24T23:27:29Z
dc.date.available2017-08-22T12:24:16Z
dc.date.available2018-11-24T23:27:29Z
dc.date.issued2017-08-01
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/266721
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3990
dc.description.abstractWe 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.
dc.languageen
dc.publisherMathematical Sciences Publishers
dc.publisherAnalysis and PDE
dc.subjectBecker–Döring
dc.subjectnucleation
dc.subjectexponential convergence
dc.subjectentropy method
dc.titleTrend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture
dc.typeArticle


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