doi:
10.3934/dcds.2009.25.1041 
Full text:
(249.7K)
Michele Coti Zelati -
Politecnico di Milano - Dipartimento di Matematica "F.Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)
Abstract:
The paper deals with the nonlinear evolution equation
ε∂ttu + $\delta$∂tu+ $\omega$∂xxxx u-$[\beta+\int_0^1[\partial_y u(y,t)]^2\d y ]$∂xxu=f,
which describes the motion of the vertical deflection of an extensible Kirchhoff beam. The existence of the global attractor of optimal regularity is shown, as well as the existence of a family of exponential attractors Hölder-continuous in the symmetric Hausdorff distance (with respect to ε) and of finite fractal dimension uniformly bounded with respect to ε.
Keywords: Extensible beam, global attractor, exponential
attractors.
Mathematics Subject Classification: 35B25, 35B41, 35B65, 37B25, 74K05, 74K10.
Received: November 2008;
Revised:
March 2009;
Published: August 2009.
