Internal null-controllability for a structurally damped beam equation

Abstract

In this paper we study the null-controllability of a beam equation with hinged ends and structural damping, the damping depending on a positive parameter. We prove that this system is exactly null controllable in arbitrarily small time. This result is proven using a combination of Ingham-type inequalities, adapted for complex frequencies, and exponential decay on various frequency bands. We then let the damping parameter tend to zero and we recover an earlier null-controllability result for the undamped beam equation.