Upper bounds of the lifespan estimates for semilinear wave equations with damping and potential in high dimensional Schwarzschild spacetime

Abstract

In this work, we study finite time blow-up phenomena for power-type semilinear wave equations in high-dimensional Schwarzschild spacetime with damping and potential terms. By carefully constructing test functions in the weak formulation of the solution, we establish blow-up results and derive sharp upper bounds for lifespan estimates.