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 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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The authors were supported by the German Research Foundation through the CRC 1060.
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Communicated by Robert V. Kohn.
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Helmers, M., Niethammer, B. & Velázquez, J.J.L. Mathematical Analysis of a Coarsening Model with Local Interactions. J Nonlinear Sci 26, 1227–1291 (2016). https://doi.org/10.1007/s00332-016-9304-y
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DOI: https://doi.org/10.1007/s00332-016-9304-y