Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Buckling and longterm dynamics of a nonlinear model for the extensible
  beam   This work is focused on the longtime behavior of a non linear evolution
problem describing the vibrations of an extensible elastic homogeneous beam
resting on a viscoelastic foundation with stiffness k>0 and positive damping
constant. Buckling of solutions occurs as the axial load exceeds the first
critical value, \beta_c, which turns out to increase piecewise-linearly with k.
Under hinged boundary conditions and for a general axial load P, the existence
of a global attractor, along with its characterization, is proved by exploiting
a previous result on the extensible viscoelastic beam. As P<\beta_c, the
stability of the straight position is shown for all values of k. But, unlike
the case with null stiffness, the exponential decay of the related energy is
proved if P<\bar\beta(k), where \bar\beta(k) < \beta_c(k) and the equality
holds only for small values of k.

25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph