Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence between radial solutions of different parabolic
  gradient-diffusion equations and applications   We consider a general form of a parabolic equation that generalizes both the
standard parabolic $p$-Laplace equation and the normalized version that has
been proposed in stochastic game theory. We establish an equivalence between
this equation and the standard $p$-parabolic equation posed in a fictitious
space dimension, valid for radially symmetric solutions. This allows us to find
suitable explicit solutions for example of Barenblatt type, and as a
consequence we settle the exact asymptotic behaviour of the Cauchy problem even
for nonradial data. We also establish the asymptotic behaviour in a bounded
domain. Moreover, we use the explicit solutions to establish the parabolic
Harnack's inequality.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas