Inertial manifold for semi-linear non-instantaneous impulsive parabolic equations in an admissible space

Abstract

In this paper, we study the existence of an inertial manifold for the solution to a semi-linear non-instantaneous impulsive parabolic equation. We present some properties of admissible Banach function spaces and introduce the definition of a φ-Lipschitz function. We use the orthogonal projection operator and the non-instantaneous impulsive operator W(·, ·) to construct the Green function G(·, ·). We give the norm estimate of G(·, ·) using Hölder’s inequality and the fractional power operator. Existence and uniqueness of solutions are established via the contraction mapping principle. We also apply this method to seek the induced trajectory. Finally we illustrate our result with an example.