Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of a homogenized two-temperature model from the heat equation   This work studies the heat equation in a two-phase material with spherical
inclusions. Under some appropriate scaling on the size, volume fraction and
heat capacity of the inclusions, we derive a coupled system of partial
differential equations governing the evolution of the temperature of each phase
at a macroscopic level of description. The coupling terms describing the
exchange of heat between the phases are obtained by using homogenization
techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France
Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138.
Pitman, Boston, London, 1982.]

10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph