Stability of vibrations for some Kirchhoff equation with dissipation
- 158 Downloads
In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval [0, T] with a tolerance level γ. The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force f. After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant.
KeywordsKirchhoff equation dissipation vibration stabilization energy decay estimate
MSC 201035B35 35L70 45K05 37L15
Unable to display preview. Download preview PDF.
- A. H. Nayfeh, D. T. Mook: Nonlinear Oscillations. Pure and Applied Mathematics. A Wiley-Interscience Publication, John Wiley & Sons, New York, 1979.Google Scholar