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Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems. (English) Zbl 0729.93023

Verf. untersuchen die exakte Steuerbarkeit von Wellen- und Plattenbewegungen durch Vorgabe der Randbedingungen. Wenn die linearen Gleichungen nur additiv um eine nichtlineare Funktion erweitert werden, lassen sich beide Probleme auf eine verallgemeinerte semilineare Operatorgleichung zurückführen. Ausgehend von der Steuerbarkeit des linearen Falles wird anstelle des Schauder’schen Fixpunktsatzes die Methode der impliziten Funktionen benutzt. Die verallgemeinerten Ergebnisse werden für beide Gleichungstypen konkretisiert.

MSC:

93B28 Operator-theoretic methods
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