We study the global existence of solutions to semilinear damped wave equations in the scattering case with power-type nonlinearity on the derivatives, posed on nontrapping asymptotically Euclidean manifolds. The main idea is to shift initial time by local existence. As a result, we could convert the damping term to small enough perturbation and obtain the global existence.
"Global existence for semilinear damped wave equations in the scattering case." Differential Integral Equations 32 (3/4) 233 - 248, March/April 2019. https://doi.org/10.57262/die/1548212431