On the stabilization and controllability for a third order linear equation
Patrícia Nunes da SilvaUniversidade do Estado do Rio de Janeiro, Rio De Janeiro, Brazil
Carlos Frederico VasconcellosUniversidade do Estado do Rio de Janeiro, Rio De Janeiro, Brazil
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 .
Cite this article
Patrícia Nunes da Silva, Carlos Frederico Vasconcellos, On the stabilization and controllability for a third order linear equation. Port. Math. 68 (2011), no. 3, pp. 279–296DOI 10.4171/PM/1892