Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed-loop control of a reaction-diffusion system   A system of a parabolic partial differential equation coupled with ordinary
differential inclusions that arises from a closed-loop control problem for a
thermodynamic process governed by the Allen-Cahn diffusion reaction model is
studied. A feedback law for the closed-loop control is proposed and implemented
in the case of a finite number of control devices located inside the process
domain basing on the process dynamics observed at a finite number of
measurement points. The existence of solutions to the discussed system of
differential equations is proved with the use of a generalization of the
Kakutani fixed point theorem.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con