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# Blow-up of solutions to semilinear wave equations with non-zero initial data

• In this paper, we are concerned with the initial value problem for $u_{tt}-\Delta u=|u_t|^p$ in $\mathbb{R}^n\times[0,\infty)$ with the initial data $u(x,0)=f(x)$, $u_t(x,0)=g(x)$, where $(f,g)$ are slowly decaying.
H. Takamura [13] obtained the blow-up result for the case where $f\equiv0$ and $g\not\equiv0$. Our purpose in this paper is to show the blow-up result for the case where the both initial data do not vanish identically.
Mathematics Subject Classification: Primary: 35L70; Secondary: 35B44, 35E15.

 Citation:

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