Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of a blow-up solution for a perturbed nonlinear heat
  equation with a gradient and a non-local term   We consider in this paper a perturbation of the standard semilinear heat
equation by a term involving the space derivative and a non-local term. We
prove the existence of a blow-up solution, and give its blow-up profile. Our
proof relies on the following method: we linearize the equation (in similarity
variables) around the expected profile, then, we control the nonpositive
directions of the spectrum thanks to the decreasing properties of the kernel.
Finally, we use a topological argument to control the positive directions of
the spectrum.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int