Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate controllabilty from the exterior of space-time fractional
  diffusive equations   Let $\Om\subset\RR^N$ a bounded domain with a Lipschitz continuous boundary.
We study the controllability of the space-time fractional diffusion equation
\begin{equation*} \begin{cases} \mathbb D_t^\alpha u+(-\Delta)^su=0\;\;&\mbox{
in }\;(0,T)\times\Omega\\ u=g &\mbox{ in }\;(0,T)\times(\RR^N\setminus\Omega)\\
u(0,\cdot)=u_0&\mbox{ in }\;\Omega, \end{cases} \end{equation*} where
$u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function
which is localized in a subset $\mathcal O$ of $\Omc$. Here, $0<\alpha\le 1$,
$0<s<1$ and $T>0$ be real numbers. After giving an explicit representation of
solutions, we show that the system is always approximately controllable for
every $T>0$, $u_0\in L^2(\Omega)$ and $g\in \mathcal D((0,T)\times\mathcal O)$
where $\mathcal O\subset(\RR^N\setminus\bOm)$ is any open set. The results
obtained are sharp in the sense that such a system is never null controllable
if $0<\alpha<1$. The proof of our result is based on a new unique continuation
principle for the eigenvalues problem associated with the fractional Laplace
operator subject to the zero exterior boundary condition that we have
established.

13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph