On the rate of convergence to equilibrium in the Becker-Döring equations

Pierre Emmanuel Jabin; Barbara Niethammer

doi:10.1016/S0022-0396(03)00021-4

On the rate of convergence to equilibrium in the Becker-Döring equations

Pierre Emmanuel Jabin
, Barbara Niethammer

Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

We provide an explicit rate of convergence to equilibrium for solutions of the Becker-Döring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-Döring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e^-ct1/3.

Original language	English (US)
Pages (from-to)	518-543
Number of pages	26
Journal	Journal of Differential Equations
Volume	191
Issue number	2
DOIs	https://doi.org/10.1016/S0022-0396(03)00021-4
State	Published - Jul 1 2003

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/S0022-0396(03)00021-4

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title = "On the rate of convergence to equilibrium in the Becker-D{\"o}ring equations",

abstract = "We provide an explicit rate of convergence to equilibrium for solutions of the Becker-D{\"o}ring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-D{\"o}ring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e-ct1/3.",

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AU - Niethammer, Barbara

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N2 - We provide an explicit rate of convergence to equilibrium for solutions of the Becker-Döring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-Döring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e-ct1/3.

AB - We provide an explicit rate of convergence to equilibrium for solutions of the Becker-Döring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-Döring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e-ct1/3.

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U2 - 10.1016/S0022-0396(03)00021-4

DO - 10.1016/S0022-0396(03)00021-4

M3 - Article

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EP - 543

JO - Journal of Differential Equations

JF - Journal of Differential Equations

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ER -

On the rate of convergence to equilibrium in the Becker-Döring equations

Abstract

All Science Journal Classification (ASJC) codes

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