Critical exponent for the semilinear wave equation with time-dependent damping
The authors discuss the initial value problem to the equation \(u_{tt}-\Delta u+b_0(1+t)^{-\beta }u_t=| u| ^{\rho }\) for \(t>0\) and \(x\in \mathbb{R}^N\) (see also [\textit{J. Lin} and \textit{J. Zhai}, Commun. Contemp. Math. 14, No. 5, 1250035, 14 p. (2012; Zbl 1255.35172)]). Under some assumptions on the initial data the non-existence of a global solution is proved for \(1<\rho \leq 1+2/N.\)
scientific article; zbMATH DE number 6104854