ABSTRACT
Abstract We study the existence of inertial manifolds for the equation ut + Au = Af(u, x) by extending the general inertial manifold theory. The problem is motivated by a boundary control system where A is a positive, self-adjoint differential operator, Af(u, x) is unbounded but Aaf(u,x) is bounded by the behavior of u for some (1/2) < a < 1. A simple example of the system is
(0)
with homogeneous boundary conditions. The example is an equation derived from a one dimensional boundary control system.
