Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence, general decay and blow-up of solutions for a viscoelastic
  Kirchhoff equation with Balakrishnan-Taylor damping and dynamic boundary
  conditions   Our aim in this article is to study a nonlinear viscoelastic Kirchhoff
equation with strong damping, Balakrishnan-Taylor damping, nonlinear source and
dynamical boundary condition. Firstly, we prove the local existence of
solutions by using the Faedo-Galerkin approximation method combined with a
contraction mapping theorem. We then prove that if the initial data enter into
the stable set, the solution globally exists, and if the initial data enter
into the unstable set, the solution blows up in a finite time. Moreover, we
obtain a general decay result of the energy, from which the usual exponential
and polynomial decay rates are only special cases.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat