This paper is concerned with the Cauchy problem for the semilinear wave equation: utt -δu = F(u) in ℝn × [0,∞); where the space dimension n ≥2, F(u) = |u|p or F(u) = |u|p-1u with p > 1. Here, the Cauchy data are non-zero and non-compactly supported. Our results on the blow-up of positive radial solutions (not necessarily radial in low dimensions n = 2; 3) generalize and extend the results of Takamura  for zero initial position and Takamura, Uesaka and Wakasa  for zero initial velocity. The main technical difficulty in the paper lies in obtaining the lower bounds for the free solution when both initial position and initial velocity are non-identically zero in even space dimensions.
|Number of pages||18|
|Journal||Differential and Integral Equations|
|Publication status||Published - 2016 Jan 1|
ASJC Scopus subject areas
- Applied Mathematics