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Index sums of isolated singular points of positive vector fields
Global and exponential attractors for the singularly perturbed extensible beam
| 1. | Politecnico di Milano - Dipartimento di Matematica "F.Brioschi", Via Bonardi 9, 20133 Milano, Italy |
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.
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