Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of a hyperplane in two-phase heat conductors   We consider the Cauchy problem for the heat diffusion equation in the whole
Euclidean space consisting of two media with different constant conductivities,
where initially one has temperature 0 and the other has temperature 1. Suppose
that the interface is uniformly of class $C^6$. We show that if the interface
has a time-invariant constant temperature, then it must be a hyperplane.

23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin