On the rate of convergence to equilibrium in the Becker–Doring equations

On the rate of convergence to equilibrium in the Becker–Doring equations Pierre–Emmanuel Jabin ? Barbara Niethammer † June 2, 2006 Abstract We provide a result on the rate of convergence to equilibrium for solutions of the Becker–Doring equations. Our strategy is to use the energy/energy–dissipation relation. The main difficulty is the struc- ture of the equilibria of the Becker–Doring 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 equilib- rium as e?ct 1/3 . Keywords: Becker–Doring equations, rate of convergence to equi- librium, entropy–dissipation methods 1 Introduction 1.1 The Becker–Doring equations The Becker–Doring equations are a system of kinetic equations to describe the dynamics of cluster formation in a system with identical particles. They can be used for example to model a variety of phenomena in the kinetics of phase transitions, such as the condensation of liquid droplets in a supersat- urated vapor. In the following clusters are characterized by their size l, which denotes the number of particles in the cluster. The concentration of l–clusters at time ?DMA, Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France, (Pierre- ) †Inst. fur Angew.

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