Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type
Authors
Dinh Van Duong
Tuan Anh Dao
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.
