Well-posedness and dynamics of wave equations with nonlinear damping and moving boundary

We studied the longtime dynamical behavior of a wave equation with critical nonlinearity and nonlinear damping in an expanding domain. First, we employed the penalty approach to establish the local well-posedness of the weak solution. Subsequently, we illustrated energy dissipation and asymptotic compactness for both the penalized equations and the original equation. Lastly, we established the existence of pullback attractors for penalized equations and the original equation.