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.
Bonaccorsi, S., Cottini, F., Mugnolo, D. (2021). Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs. APPLIED MATHEMATICS AND OPTIMIZATION, 84(3), 2849-2887 [10.1007/s00245-020-09732-w].
Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs
Cottini F.;
2021
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.
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