Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Consistency of Partial Observability for PDEs   In this paper, a new definition of observability is introduced for PDEs. It
is a quantitative measure of partial observability. The quantity is proved to
be consistent if approximated using well posed approximation schemes. A first
order approximation of an unobservability index using empirical gramian is
introduced. For linear systems with full state observability, the empirical
gramian is equivalent to the observability gramian in control theory. The
consistency of the defined observability is exemplified using a Burgers'
equation.

0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin