Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternative probabilistic representations of Barenblatt-type solutions   A general class of probability density functions \[u(x,t)=Ct^{-\alpha d}\left
(1-\left (\frac{\|x\|}{ct^{\alpha}}\right )^{\beta}\right )_+^{\gamma},\quad
x\in \mathbb{R}^d,t>0,\] is considered, containing as particular case the
Barenblatt solutions arising, for instance, in the study of nonlinear heat
equations. Alternative probabilistic representations of the Barenblatt-type
solutions $u(x,t)$ are proposed. In the one-dimensional case, by means of this
approach, $u(x,t)$ can be connected with the wave propagation.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol