An Application of Inertial Manifold Theory to Boundary Stabilization of Semilinear Diffusion Systems

This paper deals with an application of inertial manifold theory to boundary stabilization of semilinear diffusion systems on a one-dimensional domain. It is shown that a Sakawa type of controller plays an important role in the construction of an inertial manifold for the closed-loop system with a given semilinear diffusion system. This means that the use of a Sakawa type of controller reduces the stabilization problem for the closed-loop system to the one on the inertial manifold.