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Polynomial operator matrices as generators: The general case

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Abstract

Of concern are systems of linear evolution equations

$$(ACP)\dot u(t) = Au(t),u(0) = u_0 ,$$

whereu is a function with values in a product Banach space ɛ:=E n andA=(p ij (A)) is anxn matrix whose entries are polynomials in a fixed linear possibly unbounded operatorA onE. In this paper we will study the well-posedness of (ACP), i.e., we will characterize those polynomial operator matricesA generating a strongly continuous semigroup on ɛ.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen, Germany

    Klaus-J. Engel

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  1. Klaus-J. Engel
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This paper is part of a research project supported by the Deutsche Forschungsgemeinschaft (DFG).

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Engel, KJ. Polynomial operator matrices as generators: The general case. Integr equ oper theory 13, 175–192 (1990). https://doi.org/10.1007/BF01193755

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  • DOI: https://doi.org/10.1007/BF01193755

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