Topological Methods in Nonlinear Analysis

Strongly damped wave equation and its Yosida approximations

Matheus C. Bortolan and Alexandre N. Carvalho

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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.

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Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 563-602.

First available in Project Euclid: 21 March 2016

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Bortolan, Matheus C.; Carvalho, Alexandre N. Strongly damped wave equation and its Yosida approximations. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 563--602. doi:10.12775/TMNA.2015.059.

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