Localization of the limit set of trajectories of the Euler-Bernoulli equation with control. (Russian, English) Zbl 1164.74415

Ukr. Mat. Zh. 60, No. 2, 173-182 (2008); translation in Ukr. Math. J. 60, No. 2, 199-210 (2008).
Summary: 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.


74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
93B52 Feedback control
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