Blow-up for semilinear wave equations with time-dependent damping in an exterior domain
Blow-up for semilinear wave equations with time-dependent damping in an exterior domain
<p style='text-indent:20px;'>We consider the semilinear wave equation with time-dependent damping <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_{tt}u-\Delta u +\mu (1+t)^{-\beta} \partial_t u = |u|^p, \quad (t, x)\in (0, \infty)\times D^c, $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ D^c = \mathbb{R}^N\backslash D $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ D $\end{document}</tex-math></inline-formula> is the closed unit ball …