Localization of the limit set of trajectories of the Euler-Bernoulli equation with control
We investigate a differential equation in a Hilbert space that describes vibrations of the Euler-Bernoulli elastic beam with feedback control. The relative compactness of positive semitrajectories of the considered equation is proved. Constructing a Lyapunov functional in explicit form and using the invariance principle, we obtain representations of limit sets.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 2, pp 199-210.
Citation Example: Zuev A. L. Localization of the limit set of trajectories of the Euler-Bernoulli equation with control // Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 173–182.