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arXiv · 1510.07538

Exact controllability for quasi-linear perturbations of KdV

Pietro Baldi·Giuseppe Floridia·Emanuele Haus
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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 presence of quasi-linear 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, classical Ingham inequality and HUM 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.

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Pietro Baldi, Giuseppe Floridia, Emanuele Haus. 2016-11-15. Exact controllability for quasi-linear perturbations of KdV. https://doi.org/10.2140/apde.2017.10.281

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