Stability and controllability of an abstract evolution equation of hyperbolic type and concrete applications

Abstract

We consider the stability of an abstract evolution equation using Liu’s principle based on the exponential stability of the inverse problem with a linear feedback and on an integral inequality. Russell’s principle also yields some exact controllability results. Some concrete examples with new stability and controllability results illustrate the interest of our approach.

Keywords

• stability of partial differential equations of hyperbolic type
• integral inequality
• evolution equations
• liu principle