Abstract
We consider differential-algebraic equations in infinite dimensional state spaces, and study under which conditions we can associate a \(C_{0}\)-semigroup with such equations. We determine the right space of initial values and characterise the existence of a \(C_{0}\)-semigroup in the case of operator pencils with polynomially bounded resolvents.
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Acknowledgements
We thank Felix Schwenninger for pointing our attention to the concept of Wong sequences in matrix calculus. Moreover, we thank Florian Pannasch for the observation in Remark 5.9 and the anonymous referee for drawing our attention to the subject of Sobolev type equations in the Russian literature.
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Trostorff, S. (2020). Semigroups Associated with Differential-Algebraic Equations. In: Banasiak, J., Bobrowski, A., Lachowicz, M., Tomilov, Y. (eds) Semigroups of Operators – Theory and Applications. SOTA 2018. Springer Proceedings in Mathematics & Statistics, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-030-46079-2_5
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