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.
Fields of Study & Subjects
Navier-Stokes equation solutions
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Nonlinear Science
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 2
- Pages
- 31–31
- Publication date
- 5 March 2026
- Language
- EN