Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained approximate null controllability of coupled heat equation
  with periodic impulse controls   This paper is concerned with the constrained approximate null controllability
of heat equation coupled by a real matrix $P$, where the controls are impulsive
and periodically acted into the system through a series of real matrices
$\{Q_k\}_{k=1}^\hbar$. The conclusions are given in two cases. In the case that
the controls act globally into the system, we prove that the system is global
constrained approximate null controllable under a spectral condition of $P$
together with a rank condition of $P$ and $\{Q_k\}_{k=1}^\hbar$; While in the
case that the controls act locally into the system, we prove the global
constrained approximate null controllability under a stronger condition for $P$
and the same rank condition as the above case. Moreover, we prove that the
above mentioned spectral condition of $P$ is necessary for global constrained
approximate null controllability of the control problem considered in this
paper.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc