Rigorous continuum limit for the discrete network formation problem

@article{Haskovec2018RigorousCL,
  title={Rigorous continuum limit for the discrete network formation problem},
  author={Jan Haskovec and Lisa Maria Kreusser and Peter A. Markowich},
  journal={Communications in Partial Differential Equations},
  year={2018},
  volume={44},
  pages={1159 - 1185}
}
Abstract Motivated by recent papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption function constrained by a linear system on a graph. For the spatially two-dimensional rectangular setting we prove the rigorous continuum limit of the constrained energy functional as the number of nodes of the underlying graph tends to infinity and the edge lengths shrink to zero uniformly. The proof is based on… Expand
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