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.
Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs / Bonaccorsi, Stefano; Cottini, Francesca; Mugnolo, Delio. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - ELETTRONICO. - 2021:(2021). [10.1007/s00245-020-09732-w]
Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs
Bonaccorsi, Stefano;Mugnolo, Delio
2021-01-01
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.| File | Dimensione | Formato | |
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