Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up and lifespan estimates for Nakao's type problem with
  nonlinearities of derivative type   In the present paper, we investigate blow-up and lifespan estimates for a
class of semilinear hyperbolic coupled system in $\mathbb{R}^n$ with
$n\geqslant 1$, which is part of the so-called Nakao's type problem weakly
coupled a semilinear damped wave equation with a semilinear wave equation with
nonlinearities of derivative type. By constructing two time-dependent
functionals and employing an iteration method for unbounded multiplier with
slicing procedure, the results of blow-up and upper bound estimates for the
lifespan of energy solutions are derived. The model seems to be hyperbolic-like
instead of parabolic-like. Particularly, the blow-up result for one dimensional
case is optimal.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int