Random evolution equations: well-posedness, asymptotics, and applications to graphs

Stefano Bonaccorsi, Francesca Cottini, Delio Mugnolo

备注：: 28 pages, 4 figures

英文摘要：

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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