Abstract
This work presents the finite-time blow-up of solutions to the equation
u
t
t
−
Δ
u
=
a
−
k
|
u
|
p
,
in the Minkowski space. We extend the previous result of Belchev, Kepka and Zhou [E. Belchev, M. Kepka, Z. Zhou, Finite-time blow-up of solutions to semilinear wave equations, J. Funct. Anal. 190 (1) (2002) 233–254] comprehensively. Due to a modification of the so-called method of conformal compactification used by Belchev, Kepka and Zhou, we show that the solutions blow up in finite time with more relaxed initial data and extended index
p
.