Strongly damped wave equation and its Yosida approximations

Alexandre Nolasco Carvalho, Matheus C. Bortolan

DOI: http://dx.doi.org/10.12775/TMNA.2015.059

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.

Keywords


Global attractor; Yosida approximation; continuity of attractors; fractal dimension

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