Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 114, pp. 1-10.
Title: Existence of exponential attractors for the plate equations
with strong damping
Authors: Qiaozhen Ma (Northwest Normal Univ., Lanzhou, China)
Yun Yang (Northwest Normal Univ., Lanzhou, China)
Xiaoliang Zhang (Northwest Normal Univ., Lanzhou, China)
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 06, 2013.
Math Subject Classifications: 35Q35, 35B40, 35B41.
Key Words: Plate equation; critical exponent; exponential attractor.