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 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