$L^p$ asymptotic stability of 1D damped wave equation with nonlinear
distributed damping
$L^p$ asymptotic stability of 1D damped wave equation with nonlinear
distributed damping
In this paper, we study the one-dimensional wave equation with localized nonlinear damping and Dirichlet boundary conditions, in the $L^p$ framework, with $p\in [1,\infty)$. We start by addressing the well-posedness problem. We prove the existence and the uniqueness of weak and strong solutions for $p\in [1,\infty)$, under suitable assumptions on …