| Contents |
| This talk is concerned with the Cauchy problem for the semilinear wave equation:
\begin{align}
u_{tt}-\Delta u=F(u) \quad \mbox{in}\quad\mathbb{R}^n\times[0,\infty),
\end{align}
where the space dimension $n\geq 2$, $F(u)=|u|^p$ or $F(u)=|u|^{p-1}u$, 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-1995, and Takamura, Uesaka and Wakasa-2011. The main technical difficulty in this work lies in obtaining appropriate lower bounds for the free solution when both initial position and initial velocity are non-identically zero, especially in even space dimensions. |
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