Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the switching behavior of sparse optimal controls for the
  one-dimensional heat equation   An optimal boundary control problem for the one-dimensional heat equation is
considered. The objective functional includes a standard quadratic terminal
observation, a Tikhonov regularization term with regularization parameter
$\nu$, and the $L^1$-norm of the control that accounts for sparsity. The
switching structure of the optimal control is discussed for $\nu \ge 0$. Under
natural assumptions, it is shown that the set of switching points of the
optimal control is countable with the final time as only possible accumulation
point. The convergence of switching points is investigated for $\nu \searrow
0$.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex