Global nonexistence of solutions to a semilinear wave equation in the Minkowski space

This work presents the finite-time blow-up of solutions to the equation utt−Δu=a−k|u|p,utt−Δu=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 pp.