Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

@article{Labidi2005UnboundednessFT,
  title={Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation},
  author={Soraya Labidi and Nasser-eddine Tatar},
  journal={Applied Mathematics and Computation},
  year={2005},
  volume={161},
  pages={697-706}
}
We consider the Euler–Bernoulli beam problem with some boundary controls involving a fractional derivative. The fractional derivative here represents a fractional dissipation of lower order than one. We prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity. 2004 Elsevier Inc. All rights reserved. 

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