Attractors for wave equations with nonlinear damping on time-dependent space
Attractors for wave equations with nonlinear damping on time-dependent space
In this paper, we consider the long time behavior of the solution for the following nonlinear damped wave equation\begin{eqnarray*}\varepsilon(t) u_{tt}+g(u_{t})-\Delta u+\varphi (u)=f \end{eqnarray*} with Dirichlet boundary condition, in which, the coefficient $\varepsilon$ depends explicitly on time, the damping $g$ is nonlinear and the nonlinearity $\varphi$ has a critical growth. Spirited …