Strongly damped wave equation and its Yosida approximations

Abstract

In this work we study the continuity for the family of global attractors of the equations $u_{tt}-\Delta u-\Delta u_t-\varepsilon \Delta u_{tt}=f(u)$ at $\varepsilon=0$ when $\Omega$ is a bounded smooth domain of $\mathbb{R}^n$, with $n\geq 3$, and the nonlinearity $f$ satisfies a subcritical growth condition. Also, we obtain an uniform bound for the fractal dimension of these global attractors.