On global existence for semilinear wave equations with space-dependent critical damping
On global existence for semilinear wave equations with space-dependent critical damping
The global existence for semilinear wave equations with space-dependent critical damping $\partial_{t}^{2} u - \Delta u + \frac{V_0}{|x|} \partial_{t} u = f(u)$ in an exterior domain is dealt with, where $f(u) = |u|^{p-1} u$ and $f(u) = |u|^{p}$ are in mind. Existence and non-existence of global-in-time solutions are discussed. To …