Mathematical analysis of a coarsening model with local interactions
arXiv:1509.04917 · doi:10.1007/s00332-016-9304-y
Abstract
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many particles, we prove existence of solutions under a reasonable density assumption on the initial data and show that the vanishing of particles and the localized interactions can lead to non-uniqueness. Moreover, we provide a rigorous upper coarsening estimate and discuss the generic statistical properties as well as some non-generic behavior of the evolution by means of heuristic arguments and numerical observations.
Extended non-uniqueness section