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The Nonlinear Heat Equation on W-Random Graphs

Archive for Rational Mechanics and Analysis volume 212, pages 781–803 (2014)Cite this article

A Correction to this article was published on 05 November 2018

This article has been updated

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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Change history

  • 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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Authors and Affiliations

  1. Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, PA, 19104, USA

    Georgi S. Medvedev

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  1. Georgi S. Medvedev
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Correspondence to Georgi S. Medvedev.

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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

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