Issue |
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
|
|
---|---|---|
Page(s) | 1795 - 1838 | |
DOI | https://doi.org/10.1051/m2an/2023006 | |
Published online | 07 June 2023 |
Continuum limit of p-Laplacian evolution problems on graphs: Lq graphons and sparse graphs
1
Normandie Univ, ENSICAEN, UNICAEN, CNRS, GREYC, Caen, France
2
Normandie Univ, UNICAEN, CNRS, GREYC, Caen, France
* Corresponding author: Jalal.Fadili@greyc.ensicaen.fr
Received:
17
January
2022
Accepted:
14
January
2023
In this paper we study continuum limits of the discretized p-Laplacian evolution problem on sparse graphs with homogeneous Neumann boundary conditions. This goes far beyond known results by handling much more general class of kernels, possibly singular, and graph sequences whose limit are the so-called Lq-graphons. More precisely, we derive a bound on the distance between two continuous-in-time trajectories defined by two different evolution systems (i.e., with different kernels, second member and initial data). Similarly, we provide a bound in the case that one of the trajectories is discrete-in-time and the other is continuous. In turn, these results lead us to establish error estimates of the full discretization of the p-Laplacian problem on sparse random graphs. In particular, we provide rate of convergence of solutions for the discrete models to the solution of the continuous problem as the number of vertices grows.
Mathematics Subject Classification: 65N12 / 34A12 / 45G1 / 05C90
Key words: Nonlocal diffusion / p-Laplacian / sparse graphs / Lq-graphons
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.