## Journal of Applied Mathematics

### Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions

Zhao-hui Fan

#### Abstract

We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in ${L}^{2}\left(Ω\right)×{L}^{2}\left(\mathrm{\Gamma }\right)$ by proving that the corresponding semigroup satisfies the enhanced flattering property. Second, we apply asymptotic a priori estimate and obtain the exponential attractor in ${L}^{p}\left(Ω\right)×{L}^{q}\left(\mathrm{\Gamma }\right)$. Finally, we show the exponential attractor in $\left({H}^{1}\left(Ω\right)\cap {L}^{p}\left(Ω\right)\right)×{L}^{q}\left(\mathrm{\Gamma }\right)$.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 389863, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807875

Digital Object Identifier
doi:10.1155/2013/389863

Mathematical Reviews number (MathSciNet)
MR3033566

Zentralblatt MATH identifier
1266.35115

#### Citation

Fan, Zhao-hui. Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions. J. Appl. Math. 2013 (2013), Article ID 389863, 6 pages. doi:10.1155/2013/389863. https://projecteuclid.org/euclid.jam/1394807875

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