Existence of Inertial Manifolds for Partly Dissipative Reaction Diffusion Systems in Higher Space Dimensions

In this paper, we prove the existence of inertial manifolds for a partly dissipative reaction diffusion system of the form[formula]whereΩis a rectangular domain in 2or a cubic domain in 3. The proof is based on an Abstract Invariant Manifold Theorem for semiflows in a Hilbert space, which is proved by using the graph transform method. The Principle of Spatial Averaging also plays an important role in the proof.