Abstract
We study computabilty of the abstract linear Cauchy problem
du(t)/dt = Au(t), t > 0, u(0) = x ∈ X
where A is a linear operator on a Banach space X. We give necessary and sufficient conditions for A such that the operator K:x↦ u is computable. We consider continuous operators and more generally closed operators A. For studying computability we use the representation approach to Computable Analysis (TTE) [7, 1] which is consistent with the model used in [6].
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Weihrauch, K., Zhong, N. (2006). Beyond the First Main Theorem – When Is the Solution of a Linear Cauchy Problem Computable?. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_75
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DOI: https://doi.org/10.1007/11750321_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
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