Upper bounds on the coarsening rate for an epitaxial growth model

  title={Upper bounds on the coarsening rate for an epitaxial growth model},
  author={Robert V. Kohn and Xiaodong Yan}
We study a speci c example of energy-driven coarsening in two space dimensions. The energy is R jrruj+(1 jruj); the evolution is the fourth order PDE representing steepest descent. This equation has been proposed as a model of epitaxial growth for systems with slope selection. Numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t, and the energy per unit area decays like t . We prove a weak, one-sided version of the latter statement: the time… CONTINUE READING
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