Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact controllability to eigensolutions for evolution equations of
  parabolic type via bilinear control   In a separable Hilbert space $X$, we study the controlled evolution equation
\begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A\geq-\sigma
I$ ($\sigma\geq0$) is a self-adjoint linear operator, $B$ is a bounded linear
operator on $X$, and $p\in L^2_{loc}(0,+\infty)$ is a bilinear control.
  We give sufficient conditions in order for the above nonlinear control system
to be locally controllable to the $j$th eigensolution for any $j\geq1$. We also
derive semi-global controllability results in large time and discuss
applications to parabolic equations in low space dimension. Our method is
constructive and all the constants involved in the main results can be
explicitly computed.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph