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.