Files and links (1)
SubmittedOpen Access (License Unspecified), Open
Journal article
THE SEMILINEAR HEAT EQUATION ON SPARES RANDOM GRAPHS
SIAM journal on mathematical analysis, v 49(2), pp 1333-1355
01 Jan 2017
Abstract
Using the theory of L-p-graphons [C. Borgs et al., preprint, arXiv: 1401.2906, 2014; C. Borgs et al., preprint, arXiv: 1408.0744, 2014], we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value problems for the discrete models can be approximated by those of an appropriate nonlocal diffusion equation. Our results apply to a range of spatially extended dynamical models of different physical, biological, social, and economic networks. Importantly, our assumptions cover network topologies featured in many important real-world networks. In particular, we derive the continuum limit for coupled dynamical systems on power law graphs. The latter is the main motivation for this work.
Metrics
Details
- Title
- THE SEMILINEAR HEAT EQUATION ON SPARES RANDOM GRAPHS
- Creators
- Dmitry Kaliuzhnyi-Verbovetskyi - Drexel Univ, Dept Math, Philadelphia, PA 19104 USAGeorgi S. Medvedev - Drexel Univ, Dept Math, Philadelphia, PA 19104 USA
- Publication Details
- SIAM journal on mathematical analysis, v 49(2), pp 1333-1355
- Publisher
- Siam Publications
- Number of pages
- 23
- Grant note
- 1412066 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS 1412066 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000400748500018
- Scopus ID
- 2-s2.0-85018769736
- Other Identifier
- 991019168371404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied