JournalspmVol. 68 / No. 3DOI 10.4171/pm/1892

On the stabilization and controllability for a third order linear equation

  • Patrícia Nunes da Silva

    Universidade do Estado do Rio de Janeiro, Rio De Janeiro, Brazil
  • Carlos Frederico Vasconcellos

    Universidade do Estado do Rio de Janeiro, Rio De Janeiro, Brazil
On the stabilization and controllability for a third order linear  equation cover

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Abstract

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 .