Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analyticity and observability for fractional heat equation on
  $\mathbb{R}^n$   In this paper, we study quantitative spatial analytic bounds and unique
continuation inequalities of solutions for fractional heat equations with an
analytic lower order term on the whole space. At first, we show that the
solution has a uniform positive analytic radius for all time, and the solution
enjoys a log-type ultra-analytic bound if the coefficient is ultra-analytic.
Second, we prove a H\"{o}lder type interpolation inequality on a thick set,
with an explicit dependence on the analytic radius of coefficient. Finally, by
the telescoping series method, we establish an observability inequality from a
thick set. As a byproduct of the proof, we obtain observability inequalities in
weighted spaces from a thick set for the classical heat equation with a lower
order term.

5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics