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2017 Exact controllability for quasilinear perturbations of KdV
Pietro Baldi, Giuseppe Floridia, Emanuele Haus
Anal. PDE 10(2): 281-322 (2017). DOI: 10.2140/apde.2017.10.281

Abstract

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).

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Pietro Baldi. Giuseppe Floridia. Emanuele Haus. "Exact controllability for quasilinear perturbations of KdV." Anal. PDE 10 (2) 281 - 322, 2017. https://doi.org/10.2140/apde.2017.10.281

Information

Received: 23 November 2015; Revised: 20 September 2016; Accepted: 12 December 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1360.35219
MathSciNet: MR3619871
Digital Object Identifier: 10.2140/apde.2017.10.281

Subjects:
Primary: 35Q53 , 35Q93

Keywords: control of PDEs , Exact controllability , HUM , internal controllability , KdV equation , Nash–Moser theorem , observability of PDEs , quasilinear PDEs

Rights: Copyright © 2017 Mathematical Sciences Publishers

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