Lumpability of linear evolution Equations in Banach spaces

Fatihcan M. Atay; Lavinia Roncoroni

doi:10.3934/eect.2017002

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2017, Volume 6, Issue 1: 15-34. Doi: 10.3934/eect.2017002

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Lumpability of linear evolution Equations in Banach spaces

Fatihcan M. Atay^1, and
Lavinia Roncoroni^2,

1.
Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
2.
Max Planck Institute for Mathematics in the Sciences, Inselstra\ss e 22,04103 Leipzig, Germany

Received: February 29, 2016

Revised: August 31, 2016

Published: March 2018

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We analyze the lumpability of linear systems on Banach spaces, namely, the possibility of projecting the dynamics by a linear reduction operator onto a smaller state space in which a self-contained dynamical description exists. We obtain conditions for lumpability of dynamics defined by unbounded operators using the theory of strongly continuous semigroups. We also derive results from the dual space point of view using sun dual theory. Furthermore, we connect the theory of lumping to several results from operator factorization. We indicate several applications to particular systems, including delay differential equations.

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Mathematics Subject Classification: 34G10, 47D06, 34K30, 34A05, 47N70.

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