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Journal article
The Nonlinear Heat Equation on W-Random Graphs
Archive for rational mechanics and analysis, v 212(3), pp 781-803
2014
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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Details
- Title
- The Nonlinear Heat Equation on W-Random Graphs
- Creators
- Georgi S. Medvedev - Drexel University
- Publication Details
- Archive for rational mechanics and analysis, v 212(3), pp 781-803
- Publisher
- Springer Berlin Heidelberg
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000334168500003
- Scopus ID
- 2-s2.0-84897965539
- Other Identifier
- 991019170395104721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Mechanics