You need to subscribe to download the article.
We analyze the stabilization and the exact controllability of a third order linear equation in a bounded interval. That is, we consider the following equation:
where is a complex valued function defined in and , and are real constants. Using multiplier techniques, HUM method and a special uniform continuation theorem, we prove the exponential decay of the total energy and the boundary exact controllability associated with the above equation. Moreover, we characterize a set of lengths , named , in which it is possible to find non null solutions for the above equation with constant (in time) energy and we show it depends strongly on the parameters , and .