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arXiv · 1509.04917

Mathematical analysis of a coarsening model with local interactions

Michael Helmers·Barbara Niethammer·Juan J. L. Velazquez
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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.

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Michael Helmers, Barbara Niethammer, Juan J. L. Velazquez. 2015-09-16. Mathematical analysis of a coarsening model with local interactions. https://doi.org/10.1007/s00332-016-9304-y

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