We study nonautonomous linear difference equations via the corresponding abstract Cauchy problem. The domains of the associated operators are time dependent and do not contain a common core, so we have to prove wellposedness by a direct approach. In the periodic case we then investigate the asymptotics (in different topologies) of the corresponding evolution families using the Perron–Frobenius theory for positive matrices combined with spectral decomposition methods. Finally, we show how flows in time-dependent networks can be treated within this framework.
Positivity – Springer Journals
Published: Jul 30, 2011
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