A blow-up result for the wave equation with localized initial data: the scale-invariant damping and mass term with combined nonlinearities
A blow-up result for the wave equation with localized initial data: the scale-invariant damping and mass term with combined nonlinearities
We are interested in this article in studying the damped wave equation with localized initial data, in the \textit{scale-invariant case} with mass term and two combined nonlinearities. More precisely, we consider the following equation: \begin{displaymath} \d (E) \hspace{1cm} u_{tt}-\Delta u+\frac{\mu}{1+t}u_t+\frac{\nu^2}{(1+t)^2}u=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty), \end{displaymath} with small initial data. Under some …