Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-approximate controllability of evolution systems via
  resolvent-like operators   In this work we extend a variational method to study the approximate
controllability and finite dimensional exact controllability (
finite-approximate controllability) for the semilinear evolution equations in
Hilbert spaces. We state a useful characterization of the finite-approximate
controllability for linear evolution equation in terms of resolvent-like
operators. We also find a control so that, in addition to the approximate
controllability requirement, it ensures finite dimensional exact
controllability. Assuming the approximate controllability of the corresponding
linearized equation we obtain sufficient conditions for the finite-approximate
controllability of the semilinear evolution equation under natural conditions.
The obtained results are generalization and continuation of the recent results
on this issue. Applications to heat equations are treated.

17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con