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Rigorous Continuum Limit for the Discrete Network Formation Problem

  • Date October 16, 2018
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Jan Haskovec (KAUST)
  • Area Mathematics

ABSTRACT

Motivated by recent physics papers describing 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. We derive 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 go to zero uniformly. The main idea is to reformulate the discrete energy functionals as a sequence of integral functionals on an appropriate space and prove their Gamma-convergence to a continuum energy functional. Taking a formal constrained gradient flow, we derive a parabolic-elliptic PDE system and study its properties.