Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The non-viscous Burgers equation associated with random positions in
  coordinate space: a threshold for blow up behaviour   It is well known that the solutions to the non-viscous Burgers equation
develop a gradient catastrophe at a critical time provided the initial data
have a negative derivative in certain points. We consider this equation
assuming that the particle paths in the medium are governed by a random process
with a variance which depends in a polynomial way on the velocity. Given an
initial distribution of the particles which is uniform in space and with the
initial velocity linearly depending on the position we show both analytically
and numerically that there exists a threshold effect: if the power in the above
variance is less than 1, then the noise does not influence the solution
behavior, in the following sense: the mean of the velocity when we keep the
value of position fixed goes to infinity outside the origin. If however the
power is larger or equal 1, then this mean decays to zero as the time tends to
a critical value.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas