Discrete Laplacians; Evolution equations in random environments; Operator semigroups; Quantum graphs; Asymptotic behavior of solutions; Combinatorial graphs; Difference operators; Differential operators; Diffusion-type equations; Evolution equations; Steady state; Wellposedness; Control and Optimization; Applied Mathematics
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Bonaccorsi, Stefano ; Dipartimento di Matematica, Università di Trento, Povo, Italy
COTTINI, Francesca ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Milan, Italy
Mugnolo, Delio; Lehrgebiet Analysis, Fakultät Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany
External co-authors :
yes
Language :
English
Title :
Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs
The third author was partially supported by the Deutsche Forschungsgemeinschaft (Grant 397230547).Open access funding provided by Universitá degli Studi di Trento within the CRUI-CARE Agreement.
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