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Exact controllability
for quasilinear perturbations of KdV
Pietro Baldi, Giuseppe Floridia and Emanuele Haus |
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Vol. 10 (2017), No. 2, 281–322
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Abstract |
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We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in the presence of quasilinear perturbations, namely nonlinearities containing up to three space derivatives, having a Hamiltonian structure at the highest orders. We use a procedure of reduction to constant coefficients up to order zero (adapting a result of Baldi, Berti and Montalto (2014)), the classical Ingham inequality and the Hilbert uniqueness method to prove the controllability of the linearized operator. Then we prove and apply a modified version of the Nash–Moser implicit function theorems by Hörmander (1976, 1985). |
Keywords
control of PDEs, exact controllability, internal
controllability, KdV equation, quasilinear PDEs,
observability of PDEs, HUM, Nash–Moser theorem
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Mathematical Subject Classification 2010
Primary: 35Q53, 35Q93
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Milestones
Received: 23 November 2015
Revised: 20 September 2016
Accepted: 12 December 2016
Published: 23 February 2017
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Authors |
| Pietro Baldi | |
| Dipartimento di Matematica e
Applicazioni “R. Caccioppoli” Università di Napoli Federico II Via Cintia 80126 Napoli Italy |
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| Giuseppe Floridia | |
| Dipartimento di Matematica e
Applicazioni “R. Caccioppoli” Università di Napoli Federico II Via Cintia 80126 Napoli Italy |
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| Emanuele Haus | |
| Dipartimento di Matematica e
Applicazioni “R. Caccioppoli” Università di Napoli Federico II Via Cintia 80126 Napoli Italy |
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