We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.
Controllability for quasi-linear Hamiltonian NLS equations / P. Baldi, E. Haus, R. Montalto. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 264:3(2018 Feb 05), pp. 1786-1840. [10.1016/j.jde.2017.10.009]
Controllability for quasi-linear Hamiltonian NLS equations
R. Montalto
2018
Abstract
We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.
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