Null-controllability for the beam equation with structural damping. Part 1. Distributed control

Sergei Avdonin, Julian Edward, Sergei Ivanov

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi )$. The null controllability properties of the equation $$u_{tt}+{\Delta }^{2}u+\rho (\Delta {)}^{\alpha }{u}_t=F(x,t)$$ are studied. Let $T>0$, and assume…