Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Codimensional Controllability for Evolution Equations   Motivated by infinite-dimensional optimal control problems with endpoint
state constraints, in this Note, we introduce the notion of finite
codimensional exact controllability for evolution equations. It is shown that
this new controllability is equivalent to the finite codimensionality condition
in the literatures to guarantee Pontryagin's maximum principle. As examples, LQ
problems with fixed endpoint state constraints for a wave and a heat equation
are analyzed, respectively.

21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin