Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate and exact controllability of the continuity equation with a
  localized vector field   We study the controllability of a Partial Differential Equation of transport
type, that arises in crowd models. We are interested in controlling it with a
control being a vector field, representing a perturbation of the velocity,
localized on a fixed control set. We prove that, for each initial and final
configuration, one can steer approximately one to another with Lipschitz
controls when the uncontrolled dynamics allows to cross the control set. We
also show that the exact controllability only holds for controls with less
regularity, for which one may lose uniqueness of the associated solution.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph