Abstract
A Kirchhoff-type equation describing the transversal vibrations of a beam is considered. The beam is clamped to a rigid base at one part of its edge and free at the remaining part. On the free part, it is subject to a feedback involving fractional derivatives instead of the classical velocity of the deflection and angular velocity. In presence of an external nonlinear source we prove that solutions blow up at a finite time.
| Original language | English |
|---|---|
| Pages (from-to) | 71-94 |
| Number of pages | 24 |
| Journal | Journal of Dynamical and Control Systems |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2008 |
Keywords
- Blow-up
- Boundary feedback
- Fractional derivative
- Kirchhoff beam problem
- Nondissipative system
- Singular kernel
ASJC Scopus subject areas
- Control and Systems Engineering
- Algebra and Number Theory
- Numerical Analysis
- Control and Optimization
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