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Controllability conditions of linear degenerate evolution systems

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Abstract

Generalizations of well-known conditions for controllability of linear abstract autonomous systems defined on Banach spaces to the case where there is a closed non invertible operator at the derivative are established. Presence of this operator implies that suitable controllers must be chosen. If the operators entering in the equation satisfy certain hypotheses, approximate controllability by use of this class of controllers is expressed only in terms of the coefficients of the system. In particular, approximate controllability in finite time is then equivalent to approximate controllability, according to the usual definition, of a corresponding non degenerate system. This is the case, for example, when the concerned spaces are finite dimensional. Some applications to partial differential equations are given.

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Communicated by A. V. Balakrishnan

This paper was written under the auspices of the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni of the Consiglio Nazionale delle Ricerche

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Favini, A. Controllability conditions of linear degenerate evolution systems. Appl Math Optim 6, 153–167 (1980). https://doi.org/10.1007/BF01442890

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  • DOI: https://doi.org/10.1007/BF01442890

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