A fundamental solution supported in a strip for a dispersive equation. (English) Zbl 1125.35405
Summary: A fundamental solution supported in a strip \([-T,T]_t\times\mathbb{R}_x\) is constructed for a general dispersive operator in one space dimension. As a direct application we obtain the behavior as \(x\to\infty\) for the trajectories arising in the (exact) boundary controllability problem in the half-line both for the Korteweg-de Vries equation and for the Schrödinger equation.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
93B05 | Controllability |
93C20 | Control/observation systems governed by partial differential equations |