Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some characterizations of parallel hyperplanes in multi-layered heat
  conductors   We consider the Cauchy problem for the heat diffusion equation in the whole
space consisting of three layers with different constant conductivities, where
initially the upper and middle layers have temperature 0 and the lower layer
has temperature 1. Under some appropriate conditions, it is shown that, if
either the interface between the lower layer and the middle layer is a
stationary isothermic surface or there is a stationary isothermic surface in
the middle layer near the lower layer, then the two interfaces must be parallel
hyperplanes. Similar propositions hold true, either if a stationary isothermic
surface is replaced by a surface with the constant flow property or if the
Cauchy problem is replaced by an appropriate initial-boundary value problem.

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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin