Electron. J. Diff. Equ., Vol. 2013 (2013), No. 114, pp. 1-10.

Existence of exponential attractors for the plate equations with strong damping

Qiaozhen Ma, Yun Yang, Xiaoliang Zhang

Abstract:
We show the existence of $(H_0^2(\Omega)\times L^2(\Omega), H_0^2(\Omega)\times H_0^2(\Omega))$-global attractors for plate equations with critical nonlinearity when $g\in H^{-2}(\Omega)$. Furthermore we prove that for each fixed $T > 0$, there is an ( $H_0^2(\Omega)\times L^2(\Omega), H_0^2(\Omega)\times H_0^2(\Omega))_{T}$-exponential attractor for all $g\in L^2(\Omega)$, which attracts any $H_0^2(\Omega)\times L^2(\Omega)$-bounded set under the stronger $H^2(\Omega)\times H^2(\Omega)$-norm for all $t\geq T$.

Submitted November 29, 2012. Published May 6, 2013.
Math Subject Classifications: 35Q35, 35B40, 35B41.
Key Words: Plate equation; critical exponent; exponential attractor.

Show me the PDF file (259 KB), TEX file, and other files for this article.

Qiaozhen Ma
College of Mathematics and Statistics
Northwest Normal University
Lanzhou 730070, China
email: maqzh@nwnu.edu.cn
Yun Yang
College of Mathematics and Statistics
Northwest Normal University
Lanzhou 730070, China
email: yangyun880@163.com
  Xiaoliang Zhang
College of Mathematics and Statistics
Northwest Normal University
Lanzhou 730070, China
email: zhangxl258@163.com

Return to the EJDE web page