From the Becker-Doring to the Lifshitz-Slyozov-Wagner equations

Connections between two classical models of phase transitions, the Becker-Daring (BD) equations and the Lifshitz Slyozov Wagner (LSW) equations, are investigated. Homogeneous coefficients are considered and a scaling of the BD equations is introduced in the spirit of the previous works by Penrose and Collet, Goudon, Poupaud and Vasseur. Convergence of the solutions to these rescaled BD equations towards a solution to the LSW equations is shown. For general coefficients an approach in the spirit of numerical analysis allows to approximate the LSW equations by a sequence of BD equations. A new uniqueness result for the BD equations is also provided.