Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-time blow-up of a non-local stochastic parabolic problem   The main aim of the current work is the study of the conditions under which
(finite-time) blow-up of a non-local stochastic parabolic problem occurs.
  We first establish the existence and uniqueness of the local-in-time weak
solution for such problem. The first part of the manuscript deals with the
investigation of the conditions which guarantee the occurrence of noise-induced
blow-up. In the second part we first prove the $C^{1}$-spatial regularity of
the solution. Then, based on this regularity result, and using a strong
positivity result we derive, for first in the literature of SPDEs, a Hopf's
type boundary value point lemma. The preceding results together with Kaplan's
eigenfunction method are then employed to provide a (non-local) drift term
induced blow-up result. In the last part of the paper, we present a method
which provides an upper bound of the probability of (non-local) drift term
induced blow-up.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an