2018
Том 70
№ 4

# On the Possibility of Stabilization of Evolution Systems of Partial Differential Equations on $ℝ^n × [0, + ∞)$Using One-Dimensional Feedback Controls

Abstract

We establish conditions for the stabilizability of evolution systems of partial differential equations on $ℝ^n × [0, + ∞)$ by one-dimensional feedback controls. To prove these conditions, we use the Fourier-transform method. We obtain estimates for semialgebraic functions on semialgebraic sets by using the Tarski–Seidenberg theorem and its corollaries. We also give examples of stabilizable and nonstabilizable systems.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 9, pp 1556–1565.

Citation Example: Fardigola L. V., Sheveleva Yu. V. On the Possibility of Stabilization of Evolution Systems of Partial Differential Equations on $ℝ^n × [0, + ∞)$Using One-Dimensional Feedback Controls // Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1289-1296.

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