Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observability inequalities for the heat equation with bounded potentials
  on the whole space   In this paper we establish an observability inequality for the heat equation
with bounded potentials on the whole space. Roughly speaking, such a kind of
inequality says that the total energy of solutions can be controlled by the
energy localized in a subdomain, which is equidistributed over the whole space.
The proof of this inequality is mainly adapted from the parabolic frequency
function method, which plays an important role in proving the unique
continuation property for solutions of parabolic equations. As an immediate
application, we show that the null controllability holds for the heat equation
with bounded potentials on the whole space.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org