Convergence Results for a Coarsening Model Using Global Linearization

@article{Gallay2003ConvergenceRF,
title={Convergence Results for a Coarsening Model Using Global Linearization},
author={Thierry Gallay and Alexander Mielke},
journal={J. Nonlinear Science},
year={2003},
volume={13},
pages={311-346}
}

We study a coarsening model describing the dynamics of interfaces in the onedimensional Allen-Cahn equation. Given a partition of the real line into intervals of length greater than one, the model consists in constantly eliminating the shortest interval of the partition by merging it with its two neighbors. We show that the mean-field equation for the time-dependent distribution of interval lengths can be explicitly solved using a global linearization transformation. This allows us to derive… CONTINUE READING