INVESTIGADORES
DE LEO Mariano Fernando
artículos
Título:
Controllability of Schroedinger equation with a nonlocal term.
Autor/es:
DE LEO, M.; SÁNCHEZ FERNÁNDEZ DE LA VEGA, C.; RIAL, D.
Revista:
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Editorial:
EDP SCIENCES S A
Referencias:
Lugar: Paris; Año: 2014 vol. 20 p. 23 - 41
ISSN:
1262-3377
Resumen:
This paper
is concerned with the internal distributed control problem for the 1D Schrödinger equation,
i u_t(x,t) = − u_xx + α(x) u + m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree-type nonlinearity stemming from the coupling
with the 1D Poisson equation, and α(x)
is a regular function with linear growth at infinity, including constant
electric fields. By means of both the Hilbert Uniqueness Method and the contraction
mapping theorem it is shown that for initial and target states belonging to a
suitable small neighborhood of the origin, and for distributed controls
supported outside of a fixed compact interval, the model equation is
controllable. Moreover, it is shown that, for distributed controls with compact
support, the exact controllability problem is not possible.