Inertial manifolds: The non-self-adjoint case

Abstract

In contrast with the existing theories of inertial manifolds, which are based on the self-adjoint assumption of the principal differential operator, in this paper we show that for general dissipative evolutionary systems described by semilinear parabolic equations with principal differential operator being sectorial and having compact resolvent, there exists an inertial manifold provided that certain gap conditions hold. We also show that by using an elliptic regularization, this theory can be extended to a class of KdV equations, where the principal differential operator is not sectorial.