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The Nonlinear Heat Equation on W-Random Graphs

A Correction to this article was published on 05 November 2018

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Abstract

For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medvedev (The nonlinear heat equation on dense graphs and graph limits. ArXiv e-prints, 2013) justify the continuum (thermodynamic) limit for a large class of coupled dynamical systems on convergent families of graphs.

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  • 05 November 2018

    We correct and improve the main result in Medvedev, ?The nonlinear heat equation on W-random graphs?, Arch. Rational Mech. Anal., 212(3), pp. 781?803.

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Correspondence to Georgi S. Medvedev.

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Communicated by W. E

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Medvedev, G.S. The Nonlinear Heat Equation on W-Random Graphs. Arch Rational Mech Anal 212, 781–803 (2014). https://doi.org/10.1007/s00205-013-0706-9

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  • DOI: https://doi.org/10.1007/s00205-013-0706-9

Keywords

  • Central Limit Theorem
  • Random Graph
  • Continuum Limit
  • Dense Graph
  • Graph Sequence