Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifespan of solutions to a damped fourth-order wave equation with
  logarithmic nonlinearity   This paper is devoted to the lifespan of solutions to a damped fourth-order
wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta
u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up
criteria for solutions at both lower and high initial energy levels are
established, and an upper bound for the blow-up time is given for each case.
Moreover, by constructing a new auxiliary functional and making full use of the
strong damping term, a lower bound for the blow-up time is also derived.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph