Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fujita modified exponent for scale invariant damped semilinear wave
  equations   The aim of this paper is to prove a blow up result of the solution for a
semilinear scale invariant damped wave equation under a suitable decay
condition on radial initial data. The admissible range for the power of the
nonlinear term depends both on the damping coefficient and on the pointwise
decay order of the initial data. In addition we give an upper bound estimate
for the lifespan of the solution, in terms of the power of the nonlinearity,
size and growth of initial data.

24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas