Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unique continuation property for a class of parabolic differential
  inequalities in a bounded domain   This article is concerned with the unique continuation property of a forward
differential inequality abstracted from parabolic equations proposed on a
convex domain $\Omega$ prescribed with some regularity and growth conditions.
Our result shows that the value of the solutions can be determined uniquely by
its value on an arbitrary open subset $\omega$ in $\Omega$ at any given
positive time $T$. We also derive the quantitative nature of this unique
continuation, that is, the estimate of a $L^2({\Omega})$ norm of the initial
data on $\Omega$, which is majorized by that of solution on the bounded open
subset $\omega$ at terminal moment $t = T$.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th