Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-global weak stabilization of bilinear Schr\"odinger equations   We consider a linear Schr\"odinger equation, on a bounded domain, with
bilinear control, representing a quantum particle in an electric field (the
control). Recently, Nersesyan proposed explicit feedback laws and proved the
existence of a sequence of times $(t_n)_{n \in \mathbb{N}}$ for which the
values of the solution of the closed loop system converge weakly in $H^2$ to
the ground state. Here, we prove the convergence of the whole solution, as $t
\rightarrow + \infty$. The proof relies on control Lyapunov functions and an
adaptation of the LaSalle invariance principle to PDEs.

7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ