## Error estimates for inconsistent load lumping approach in finite element solution of differential equations

- Pradeep Kumar Gudla, Ranjan Ganguli
- Applied Mathematics and Computation
- 2007

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@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} }

- Published in Applied Mathematics and Computation 2005
DOI:10.1016/j.amc.2003.12.057

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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