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arXiv · 1803.02210

Special solutions to a non-linear coarsening model with local interactions

Constantin Eichenberg
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Abstract

We consider a class of mass transfer models on a one-dimensional lattice with nearest-neighbour interactions. The evolution is given by the discrete backward fast diffusion equation, with exponent $β$ in the regime $(-\infty,0) \cup (0,1]$. Sites with mass zero are deleted from the system, which leads to a coarsening of the mass distribution. The rate of coarsening suggested by scaling is $t^\frac{1}{1-β}$ if $β\neq 1$ and exponential if $β= 1$. We prove that such solutions actually exist by an analysis of the time-reversed evolution. In particular we establish positivity estimates and long-time equililibrium properties for discrete parabolic equations with bounded initial data.

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Constantin Eichenberg. 2018-03-06. Special solutions to a non-linear coarsening model with local interactions. https://doi.org/10.1007/s00332-018-9519-1

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