Journal article
Evolution equations on co-evolving graphs: long-time behaviour and the graph continuity equation
- Abstract:
- We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the so-called graph-continuity equation are shown to be the push-forward of their initial datum through the flow map solving the associated characteristics' equation, which depends on the co-evolving graph considered. This connection can be used to prove contractions in a suitable distance, although the flow on the graphs requires a too limiting assumption on the overall flux. Therefore, we consider upwinding dynamics on graphs with pointwise and monotonic velocity and prove long-time convergence of the solutions towards the uniform mass distribution.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 770.9KB, Terms of use)
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- Publisher copy:
- 10.1007/s00332-026-10248-w
Authors
- Publisher:
- Springer
- Journal:
- Journal of Nonlinear Science More from this journal
- Volume:
- 36
- Issue:
- 2
- Article number:
- 31
- Publication date:
- 2026-03-05
- Acceptance date:
- 2026-02-07
- DOI:
- EISSN:
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1432-1467
- ISSN:
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0938-8974
- Language:
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English
- Keywords:
- Pubs id:
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2120969
- Local pid:
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pubs:2120969
- Deposit date:
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2026-02-07
- ARK identifier:
Terms of use
- Copyright holder:
- Carrillo et al.
- Copyright date:
- 2026
- Rights statement:
- Copyright © 2026, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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