Random evolution equations: well-posedness, asymptotics, and applications to graphs
Dynamical Systems
2020-04-28 v1 Probability
Abstract
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for pathwise convergence in norm of the (random) propagator towards a (deterministic) steady state. We apply our findings in two environments with randomly evolving features: ensembles of difference operators on combinatorial graphs, or else of differential operators on metric graphs.
Cite
@article{arxiv.2004.12971,
title = {Random evolution equations: well-posedness, asymptotics, and applications to graphs},
author = {Stefano Bonaccorsi and Francesca Cottini and Delio Mugnolo},
journal= {arXiv preprint arXiv:2004.12971},
year = {2020}
}
Comments
28 pages, 4 figures