The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimen- sional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.

Exact controllability of infinite dimensional systems with controls of minimal norm / Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 54:2B(2019), pp. 1001-1021. [10.12775/TMNA.2019.087]

Exact controllability of infinite dimensional systems with controls of minimal norm

Malaguti, Luisa;Perrotta, Stefania;Taddei, Valentina
2019

Abstract

The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimen- sional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.
54
2B
1001
1021
Exact controllability of infinite dimensional systems with controls of minimal norm / Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 54:2B(2019), pp. 1001-1021. [10.12775/TMNA.2019.087]
Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1187430
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