Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internal controllability of parabolic systems with star and tree like
  couplings   We consider systems of parabolic equations coupled in zero order terms in a
star-like or a tree-like shape, with an internal control acting in only one of
the equations. We obtain local exact controllability to the stationary
solutions of the system, under hypotheses concerning the supports of the
coupling functions. The key point is establishing Carleman estimates with
appropriate observation operators for the adjoint to the linearized system,
which allows the study of the controllability problem, in either linear or
nonlinear cases, in an $L^\infty$ framework.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg