Long time behavior of semilinear wave equation with localized interior damping term under acoustic boundary condition

This paper is concerned with the long time dynamics of the semilinear wave equation including localized interior damping term under acoustic boundary conditions. With appropriate assumptions, the existence of a global attractor for the semigroup generated by the considered problem is proved. Moreover, imposing more strict conditions on the nonlinearity in the equation, the regularity and finite dimensionality of the attractor are established.