English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Using the theory of $L^p$-graphons (Borgs et al, 2014), we derive andrigorously justify the continuum limit for systems of differential equations onsparse random graphs. Specifically, we show that the solutions of the initialvalue problems for the discrete models can be approximated by those of anappropriate nonlocal diffusion equation. Our results apply to a range ofspatially extended dynamical models of different physical, biological, social,and economic networks. Importantly, our assumptions cover network topologiesfeatured in many important real-world networks. In particular, we derive thecontinuum limit for coupled dynamical systems on power law graphs. The latteris the main motivation for this work.

The semilinear heat equation on sparse random graphs