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March  2017, 6(1): 15-34. doi: 10.3934/eect.2017002

## Lumpability of linear evolution Equations in Banach spaces

 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  March 2016 Revised  September 2016 Published  December 2016

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.

Citation: Fatihcan M. Atay, Lavinia Roncoroni. Lumpability of linear evolution Equations in Banach spaces. Evolution Equations & Control Theory, 2017, 6 (1) : 15-34. doi: 10.3934/eect.2017002
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