This work is devoted to studying a wave equation with degenerate nonlocal nonlinear damping and source terms. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping of polynomial type when the initial energy is small. Also, we firstly derive some sufficient conditions on initial data which lead to finite time blow-up.

The initial-boundary value problem for a wave equation with nonlinear averaged damping and nonlocal nonlinear source term is considered. We provide the sufficient conditions of finite time blow-up fo...