Topological Methods in Nonlinear Analysis

Strongly damped wave equation and its Yosida approximations

Matheus C. Bortolan and Alexandre N. Carvalho

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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.

Article information

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

Dates
First available in Project Euclid: 21 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458588652

Digital Object Identifier
doi:10.12775/TMNA.2015.059

Mathematical Reviews number (MathSciNet)
MR3494959

Zentralblatt MATH identifier
06700563

Citation

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. https://projecteuclid.org/euclid.tmna/1458588652


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