Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two analytical formulae of the temperature inside a body by using
  partial lateral and initial data   This paper considerers the problem of computing the value of a solution of
the heat equation at a given point inside a bounded domain after the initial
time. It is assumed that the initial value of the solution inside the domain
(possibly in a part of the domain) is known; the boundary value and the normal
derivative on a part of the boundary of the domain over a finite time interval
are known. Two analytical formulae for the problem are given. Both formulae
make use of a special fundamental solution having a large parameter of the
backward heat equation.

26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas