Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type

Abstract: In this paper, we consider the semilinear damped wave equation with nonlinearities of derivative type $|u_t|^p$. We observe that this problem admits a unique global (in time) solution with small initial data for all $p > 1$ in low spatial dimensions $n=1,2$. This result provides new insights into semilinear damped wave equations and complements the existing literature.